{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# TD - Introduction à Numpy & Matplotlib \n", "\n", "L'objectif de ce TD est de se familiariser avec les principales librairies numériques de Python, à savoir [numpy](https://docs.scipy.org/doc/numpy/reference/), [scipy](https://docs.scipy.org/doc/scipy/reference/) et [matplotlib](http://www.matplotlib.org). \n", "\n", "Vous importerez ces bibliothèques avec les instructions suivantes:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy.stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les parties notées « **Pour aller plus loin** » sont à traiter chez vous ou à la fin du TP si le temps le permet.\n", "\n", "**IMPORTANT:** n'oubliez pas d'ajouter des commentaires à votre code." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rappels Matplotlib\n", "\n", "La fonction de haut niveau [plt.subplots](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplots.html) permet de générer, dans son utilisation la plus simple, une figure (`fig`) et un \n", "système d'axe (`ax`):\n", "\n", "```python\n", "fig, ax = plt.subplots(1, 1) # Figure à 1×1=1 syst. d'axes\n", "```\n", "\n", "* `fig` est un objet de type `Figure` contenant un (ou plusieurs) système(s) d'axes, et pouvant être affiché ou sauvegardé (p.ex. au format PDF ou PNG);\n", "* `ax` est un objet de type `Axes` disposant de nombreuses méthodes de visualisation (`plot`, `scatter`, `imshow`, `hist`, etc.), et de personalisation (`xlabel`, `xscale`, `title`, `legend`, `grid`, etc.).\n", " \n", " \"Anatomie" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracé de courbes (1D)\n", "\n", "### Figure de diffraction par une fente fine\n", "\n", "La répartition de l'intensité lumineuse d'une onde monochromatique diffractée par une fente fine de largeur $a$ est:\n", "$$\n", "I(\\theta) = I_0 \\,\\sin_c^2\\left(\\frac{\\pi a \\sin \\theta}{\\lambda}\\right)\n", "$$\n", "\n", "où $\\lambda$ est la longeur d'onde, $\\theta$ l'angle au centre et $I_0$ l'intensité au centre de la figure de diffraction.\n", "\n", "Nous allons tracer l'allure de la fonction $I/I_0$ en fonction de $x = (\\pi a \\sin \\theta)/\\lambda$.\n", "\n", "* Générer un vecteur $x$ de 200 points entre $\\pm 4\\pi$ (à l'aide de la fonction \n", " [numpy.linspace](https://numpy.org/doc/stable/reference/generated/numpy.linspace.html))\n", "* Génerer le vecteur $y = \\sin_c(x)$ (utiliser \n", " [numpy.sinc](https://numpy.org/doc/stable/reference/generated/numpy.sinc.html) $=\\sin(\\pi x)/(\\pi x)$)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(-4 * np.pi, +4 * np.pi, 200)\n", "y = np.sinc(x / np.pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Dans une figure à un système d'axe, tracer conjointement $y$ et $y^2$ en fonction de $x$.\n", "* Agrémenter la figure pour la rendre compréhensible (titre de la figure et des axes, légende, etc.).\n", "* Sauvegarder la figure au format PDF (utiliser [plt.savefig](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.savefig.html))" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1)\n", "ax.plot(x, y, label='sinc') # Tracé y(x)\n", "ax.plot(x, y**2, label=u'sinc²') # Tracé y²(x)\n", "ax.set(title=u'sinc et sinc²', # Titre et intitulé des axes\n", " xlabel=r'$x = (\\pi a \\sin\\theta)/\\lambda$', ylabel=r'$y = I(\\theta)/I_0$')\n", "ax.legend() # Légende\n", "plt.savefig(\"diffraction.pdf\") # Sauvegarde au format PDF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Pour aller plus loin\n", "1. Modifier le code pour prendre en compte une largeur de fente et une longueur d'onde précise.\n", "2. En choisissant différentes valeurs de $a$ et $\\lambda$, tracer sur une même figure l'évolution de la figure de diffraction:\n", " * pour des largeurs de fentes différentes, à une seule longueur d'onde, \n", " * pour différentes longueurs d'onde, avec une fente de largeur fixée. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trèfles de Habenicht (courbe polaire)\n", "\n", "Les trèfles de Habenicht sont des courbes «ornementales» en représentation polaire, d'équation\n", "$$\n", "r_n(\\theta) = 1 + \\cos n\\theta + \\sin^2 n\\theta, \\qquad n\\in \\mathbb{N}^*\n", "$$\n", " \n", "* Définir la fonction `habenicht(n, theta)` permettant de calculer $r_n(\\theta)$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def habenicht(n, theta):\n", " \n", " return 1 + np.cos(n * theta) + np.sin(n * theta) ** 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Générer un vecteur $\\theta$ de 200 points entre 0 et $2\\pi$.\n", "* Génerer les tableaux 1D `r3`, `r5` et `r7` des valeurs de $r_n(\\theta)$ pour $n = 3, 5, 7$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "theta = np.linspace(0, 2 * np.pi, 100)\n", "\n", "r3 = habenicht(3, theta)\n", "r5 = habenicht(5, theta)\n", "r7 = habenicht(7, theta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Rappel\n", "\n", "Pour tracer une courbe en coordonnées polaires, il faut un système d'axes adapté:\n", "\n", "```python\n", "fig = plt.figure() # Création de la figure seule\n", "ax = fig.add_subplot(1, 1, 1, projection='polar') # Ajout d'un syst. d'axes en polaire\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Tracer dans un même système d'axes les différentes courbes polaires $r_{n=3,5,7}(\\theta)$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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iRSxP1l0khBAarVb7tLe390MLFixwvPfeey3qs5a1y3dp3/Frxq+M8hrFaO/RBDoFEugYiJ+9HxYKC1YkfMv7Ce8g2b3BmJE3MDJkcIfHtfzwcnZn7WbekHkdEmEAC6WC127rj5eTmg9PurIp9QBjDJlQcALu+LLrIgzmyIpJb0JhGvz4L9D2Bp/orvfXCVQqFQ8++KDlPffco1uyZMlz77777sN2dnYvVlRUfCpJUodK3MjI9ASya6KHEUIIe3v7v7m7u5985pln/i81NdX1vvvu67AIg9nytbGw4Z1r3+GxyMeY3HsyIdoQrFXWpOVVsfxnV1TZzzHZ9y7iCrcx+bvJrDi8ghpD28bcvqx9vJ/wPjf2vpE7g+/s8HhMJhN6vZ4HhnvjrAokvTwZn1NfY/IYSI3/9dTV1WEytVsxvHWUFmZBt/eC1XdBfkrX++oCarWaefPmaZKTkz3uv//+xTqd7qSlpeW1f+ogZM7HZDKZ2r5tvIKpP7cmPxjZNdGDCCE83NzcVl977bUR7733noOjo2OX+nn94Ot8l/Yd++/a32T7qYJK7vjodxQCVs8Zhr+LDZllmSw+tJjfzvyGp40nj0c+zkDdQNQWajQqTeMS5ZyKHO746Q5c1C58NekrNBYaTCYTFRUVVFVVNT6qq6upq6tDr9c3HlehUKBSqVAoFPxwbjs/lX7Npswsyga9Rpk2HKPRiMFg4PzvkqWlJVZWVqjVatRqNRqNBltbWzQaTeuRHPkn4PMbwaiH6V+B38gufX7dJTMzk7vuuqsoJSVlY15e3kPySr0/l8TExB/d3d37urq6lioUiqtKoEwmk8jPz3c4d+5cckRExJSG7bIQ9wBCCGFnZ3evg4PD6ytWrHCZMGFCt+40FsUsYk3KGg7efbBxW1ZJNbd/sI8ag4k1Dw4lUNd0gu1gzkFej3mdlOKm1qSFwgKNhQaDySyUr4e9jqZOQ1VVFUIIbGxssLGxQaPRoNFoUKvVWFlZoVKpWhTM5OwD3Ln1fv52zoaRt//MkN7N44olSUKv11NTU0N1dTXV1dVUVlZSWVlJVVUVALa2tjg6OuLg4ICjo+MfGeKKT8NXd0BROkx9t+d8xpIEFXlQfMrcd0Uu9L0ZtP6tNJf4+OOP6+bPn5+fn58/02g07uiZgci0x6FDh3QqlepjoB9X3127CThiMBjuj4yMzGvYeMUJsRDiU2AykCdJUr/6bQuBqZhPMg/4myRJ2UKIMcAPwKn63ddLkvRy/T7Tgf8DvpQkaWk3xuPu5ua2ety4cREffPCBY2eXIrfEW4feYmXySuJmxQGQV17DHR/+TmFlHd88MJR+Xi0fw2gysjtrN/lV+ZRWlVJYVkhRRRHlNeUYhZHrva5nqPdQHBwcsLGxaTPGuDX0W19k2Nl12JYPwNI4h58fGYWFsnO/lQZLvLS0lJKSEkpKSjAajTg6OuLs7IyrnQXW398Pp3fDmGfNURmdGWvJGXN8c94xs+gW1YuvvhKAfWprTlmouKXaiGbkkzDiEVBZtdhVZmYmM2bMKEpLS/s5Nzf3Hz1lHQshlEAskCVJ0mQhxOfAaKC0vsnfJElKqF/y/jkQCDwgSdLRnji+zOXFlSjE1wAVmAW0QYjtJUkqq3/9CNBXkqS59UL8lCRJk1vo53vgNuAr4P7O/sCEEMLW1naWo6Pjm8uXL3eZOHFij1253457m0+PfErCPQkUV9Yxffl+MourWDl7CJG+Ti3uYzAYyM/PJzc3l+LiYjQaDa6urmi1Wuzt7buUoa0ZFXmwNJx7fP3JwoWTR+fy/I2h3D+qd7e7NhqNlJaWUlBQQEFBAfqaSvpnfIo2YyNS/9sRETPA0RccvMHivBA9STJP9GXsNYtvxj5zXDOAwgKc/MwTgPWPDcZC5qetxiiZcELFPUUFzFC6YHPjYnM4XQtIksSKFSvqXnjhhbyCgoKZBoNhZ3fPVwjxBDAYsD9PiH+SJGndBe0mAAHAOuC/kiTd191jy1x+XHFRE5Ik7RJC+F2wrey8P20wF7ZsjwYTSzrvdYcQQri5ubmtHjt27IAPP/ywR6zg81EqlBglI8WVtcz69CCnCiv5/G9RzURYr9fTUI6ouroanU6Hj48P4eHhPSO8F5K+AwzV9PcZRVLGVsaEaHlrawqTwz1xd2g/frktlEplY2WPPn36YDQaKSwI59xOT9yTPoaktX80ttGBow+otZCTCJV5f2z3HQ7DHzE/60JB8cck6dqUtSz8/V2i3aOZEz6Hz45+xjL28LnJwD0/3stdXmOwnfA62Hs2GZsQgjlz5lhOnDjRe/r06evd3Nx+ysvL+4ckSZVdOVchhDdwI/Aq8ER7Hw3mOz0Tnfyeylw5XHFC3BpCiFeBezDf2o09761hQohEzMUrnzrv1m495lvDVZIkdXiNrUajucnLy+vj5cuXu0yaNOmi+K8Uwtzt9BX7OFVQw0czIxke6AKYb+tzc3PJzMykuroaDw8PwsLCsLXtWmrJTpEdDyo1/XuNwZCxiVmjLPk9TeKVn5N5965BPXoopVKJzs0N7liMVPYkFWeSKD2TRF3eSexNpdhLJViUZyMCxoLvCPPDOaBVF8YXR79gUewirvG+hiVjlmCltCLaI5qk/CQ+THifdxR7+KIijle+nsLYubEt9uHj48OePXu0y5cvv/PFF18cK4SYKklSfBdObylmt9iFK2leFUK8APwGPFOf+H4LsArzd3tOF44lcyUgSdIV9wD8MBebbOm9Z4EF9a/tAdv615OA1G4cU7i4uCwYMmRIYUFBgXQxWXLwfanf5/2k4Od/lHal5EmSJEnl5eVSUlKStG3bNunIkSNSaWnpRR1Di3xygyR9fL2UVZ4l9fu8n/TNsW+kpVtTJN+nf5L2pOb/KUMwmUxSQUGBFB8fL23fvl06fvy4VF1d3Wb79xPMn+cT25+Q6gx1LbY7UnBEumHlEOnvHwRKktHY7jhSU1OlgICAAjs7uxlS575Hk4H361+PweyOAHMlbQFYAV8AL3SmX/lxZT+uthlJMPt8bwOzy0Kq9/1KkrQRsBBCuHS2QyGEWqfTbbj55psf2717t9bZuYUMZD1ETmk13x7MAuDDWQMIsjPy+++/c/jwYbRaLaNHjyYsLAx7e/t2euphTEazG8BzIB42Htgp7EgqSOLB0b3ppdWw6JcTf8owhBA4OzszYMAARo4cibW1NQcPHiQ2NpaioqImbSVJYsmhJbyf8D5TA6byxjVvYKFsuX5fmHMYQ218SLW0QKopbbHN+QQGBhIXF+ccGRn5nk6nW1w/qdYRRgBThBCngdXAOCHEKkmSciQztcBnwJ+zqkXmsuCqEOILsmlNBY7Xb3cX9aEBQohozOdb2Mm+vVxdXeMWLFgwfsWKFfYXsxDnqYJK7vxoPxW15kVd1WePkJubS79+/Rg+fDienp4Xx/fbEfJPgL4KPAcihMDPyo/D+YextlAyI7oX8WdKOFtc9acOSaVS4evry6hRo+jduzfp6ens2bOHnJwcjCYjr+x/hc+Pfs6MkBm8POJllIq2F9UE2npTolRSWHqqzXYN2Nvb8+uvvzrNnDnzAZ1O92t9Be02kSTpWUmSvCVJ8gOmA9skSZophPAA8yQwcDPQYq0zmauTK06IhRDfAL8DwUKIs0KI2cBrQogjQojDwPXAo/XNpwFH6n3EbwPTJUnqcJiIEGKIh4dH7Lp164Lnzp3bcnxTDyBJEmtiM7nx7d2UVNYyxsvsuo8cHElERARdzU/co2TXu0I9BwLga+XL6bLTlNaWcmN/DwA2JbWaB/uiIoRAq9UyePBgBg4cSE5uDnPWz2FNyhpm95vNs9HPNvrd2yLQwRz9kVbQ8QgxpVLJkiVL7BYvXjxCp9MlCCFaDkxun6+EEElAEuACvNLFfmSuQK64yTpJkma0sPmTVtq+C7zbleM4ODjMDg4Ofn3Lli3Ovr49l7j8Qkqr9Ty3/jA/J50jxEnB/Ot7kW7Rh52HQGV5Gf17suPNyd+dAwHws/QDzAmKhnsNp5+XPT8n5fDANd0PZesOltaWrCpZxcHKg9zheQcDKwaSk5ODh4dHu3HTgU7BAJwsTmVoJ487c+ZMy+Dg4IBbbrllv6Wl5fS6urrt7e0jSdIOYEf965Zj52T+ElxxFvHFRgih1Ol0HwwbNmxRbGzsRRXhA+mF3LBkB5uPnOPvg7R8/9i1jBgYhpWF2fg2mi6jvDPZ8eA5oDFncC+rXggEhwsOAzCpvwcJmX++e+J8agw1PLL9EbZmbOXpqKeZf918oqOjyc/PZ+/evc18yBfi7OiHo9FIallGl44fFRVFTEyMLiQkZJ1Wq32sS53I/CWRhfg8hBBWrq6uW++///5ZGzdudLxYIWGHMoqZ/dl+pi/fD5KRb2YP5sU7hmFtZa6W3HAbbbxcEoAZ9XAuySzE9agVano79CapIAngkrsnKvWVPPTrQ+zN2suC4QuY2XemeZxqNREREURERJCamkpMTAzV1dUt9iE0WgLr9KRVdb2akoeHBwcPHtSOHTv2JTc3tw9Fe2a4jAyyEDdSHxmxbd68eUP/85//2PT0pJjRJLH5SA63vr+X2z7Yx/70Iu4b5s2v/x5PdKBbk7aOVuZkQZnlbVb8/vPISwZjbaN/uIH+rv1Jyk9CkiR8nW0a3RN/NqW1pcz5ZQ7xefG8Nuo1bg26tVkbOzs7hgwZgq+vLwcOHCA1NbV5xjhrRwL0ek7WFNKJqYRmWFtbs3btWocpU6bM0Ol0n3ciokLmL8pl5IS8dAghbFxdXXcsXLiw/5w5c5pPyu19G+K+BFsd2LmDnUfTZ1t387NVUwtakiSO5ZSzIyWPb2MyySiswlUteHSkBw+M74+tdcsRGMM9h2OttGbL6S1EuUddlHPuFBdM1DXQ36U/36d9z9mKs/jY+TCpvwdvbD7B2eIqvJ26ULGjC5TVlTF7y2zSS9NZMmYJ43q17WrV6XQ4Oztz8uRJdu/eTf/+/dFq62vtKVUEmVRUSHpyKnPwtPVss6+2UCgULF++3F6tVt+yevVqayHEXZKc41imFf7yQiyEsHN1dd2zaNGikHvuuceyWYPjP8PW+eBVX9o+Ox7KNoKhhdtbt/6U3/AWuyq82XEij50p+eSV1wLQR6viqWGO3Hd9JBp128uBNRYaRvuMZmvGVp6JfqYxleUlIzserB3BqWlAQENi+aT8JHzsfLixXog3JZ370ybt3ol7h9SSVN6/9n1GeI3o0D5KpZI+ffrg6elJYmIi9vb2hIaGolKpiBTm/83/Uv/Hvwb+q1tjE0KwbNkyO41GM+nzzz//QQhxsyTVl1uRkTmPv7QQCyFs3Nzc9j300ENhd955Z3NfXuFJ+G6u2RL828Y/ks1IEtSWQfk5KgrPknH6JPln0+mfvQaHL64nzTiV31S3M6yPBwN0ljjrcxk+MAx3d/cOj22i30S2nN7CwXMHGe45vKdOuWtkx5s/gwvcnYGOgahVapIKkpjUexK+zjaEef550RPHCo+xJmUN04Ond1iEz8fW1pbhw4eTkZHBnj17GODvQmBRJtd7jGJV8iruDr0brXUHKlO3gRCC5557zragoGDCTz/99H39smjZMpZpwl/WdyWEULu6uu588803+zz00ENi//791NbW/tGgrhK+nWVOGnPHl40iXFqtZ+ORc7z0y1kmfp1H/y9quHGHFw+cuoYnnD/ghG4Cj6q+I9btP/zL6xQR9lXcOG5kp0QYYKT3SGwsbNh8anNPnnbn0ddAbnIztwSASqEiVBvaGDkBcGP4nxM9YZJMvHrgVRytHHl44MNd7kcIgZ+fH4MHD6Zo98cA/CPqKWqMNXya9Gm3x1lWVsahQ4dYsmSJ8t577x3t6ur6tewzlrmQv+QXoj464rdXX32136xZsyx1Oh2hoaE0irFUX9AyLxlu+5giC3e+jTnDvZ8eZPArW/nHV3F8G5OJ1saCx67twzcPDCXppRv44uEbCHv4G6qnfoKh+CzBO+cQVb0TK1XHyyQ1YKW04tpe1/LrmV+pM9ZdhE+hg+QeBZO+RSEGs3vieOFx9EZzRY8/K3rih7QfSMxP5MnBT2Jv2f3l3ra2tvhXHKJa25fcbEsm+k5k9YnV5FXZN6MSAAAgAElEQVTltb9zKzSIcGRkJPb29rz22mu206dPn6jT6T6ToylkzucvJ8RCCAtXV9ctzz///MAHHnigcWLufDHWx3wGh78lIfAh7t5hS9Srv/L0/5JIL6jg7yP8WTd3GIdfup6v7h/Ko+ODGBbgjLWFWWzPnj3LgVIXau7bgQidgtj+CnwyHvKOd3qsE/wmUF5Xzr7sfT33AXSWbHNy+taEOFQbSp2pjtNlpwEa3RObj148IS6tLeWtQ28xUDeQm3rf1DOd5qcgzh1GHTWLwMBAIusiMZgMLD+8vEvdXSjC8IfPeOrUqTfrdLoPembgMlcDfzkfsU6nW/HQQw9FPfLII81mzHQ6HeU1BlJXPY+F5MUtR4bj71LD3NG9mdjPgzBP+1ZXZ5lMJpKTk6mqqmLEiBHm0j+3fwZ9p8BPT8BH18C4eTDsn01y5LbFUM+hOFo5svHURsb4jOnWeXeZ7ATQuJgTsreAjYUNQJPCpdH+Wr6NyUSSpC5VAWmPd+LfobSulHlD5vVc/0fWAQLCbkFnr2PyyMls37SddSnrOF16Go2FxvxQmR82FjZoLDSoVWoslZZYK62xUlphpbLCWGMkPTWdAWEDKFeUYyvZNsaGCyH48MMP7QsLC6drtdrjRUVFXa4OI3P18JcSYq1W+89Ro0ZNffHFF5vFVhlNEt/GZLL4lxOs1edTYO3Lj7OH089H2+6PXa/XExsbi1arJSoqqmn7sFvMuXJ/ehy2vmCOwrj5A3Pu3HawUFhwne91/JT+E1X6KjQWf05IWBOy45G8BmE0GpsUFDWZTOaFEfXTTnWmP9wnAa62VNUZOVdWg4eDukeHk1yYzJoTa7gr9C6CtcE906kkQdI68B8F9mbXilqt5qXrX+K5X5+juKyYEqsSKvWVVBmqqDZUU91S1MyF1N8U3N//fh4d9GjjZoVCwVdffeUQHR0939LSMrEjy6Flrm7+MkKsUqlGhYSELFi9erXjhcK6P72QBRuSOZZTRpSvI34FRbiHTiLm1BHq3IZiZdV6vp+qqipiYmLo06cPHh4eLTey1cGdq8xVJjY+BR+MgPEvQvSDjUuGW2Oi/0TWpqxlV9YuJvhN6PR5dwS9Xk9FRUVjgc+GIp+m2kpG5R0jQ92Ps/v3NykoWl1dzeHDh8moNC8HjomLoVxtzq9fVZ9Fclf8CUb10TUWKFWpuvd1a5ig01pr+ceAf3SrrybkJEDRSRjxaJPNOlsdK6auID09ndzcXKKiohqLnBpNxkZBrjHWUGuopaisiMPJh/EL8kNpqaTWWMs78e9wrOhYs0NaW1uzefNmbXR09GohxFBJkjqW8k3mquQvIcRCCF9PT891mzdv1qrVf1hoeqOJf69N5PuEbLwc1bx710Bu9FciFtei8Qwm1N/sMx46tGUxLi4uJiEhgQEDBuDk1HItufMGAeF3gN8o2PAIbH4Gjv1krlTcSiVhgEG6QbiqXdl8anOPCLHRaKSsrIzi4mKKi4spLy9HpVJha2uLjY0NdnZ2uLu7o9FoUOUcQuw24Tf8FvyCm5a237FjB0OGDEGTr4FMCO0Xymif0UiSRGBRBf/5fRfnqqC8vJxz585RUVGBJEk4ODjg5OSEk5MTdnZ2nXIt/JD2A4fzD/Ofkf/pkQm6RpLWmevb9Z3S7C0hBAEBAajVavbt20dUVBQajQalQomtpS22luZFPGVlZWSmZ3LHiDua5Ir+JeMXUotTWzysp6cn3333nW7y5MlbhRADpU5UipG5urjqhbh+1dzW//3vfzpv7z/8nJIk8dKPR/k+IZt/jQvk4bGB5gm3s4fMDRx80Ol0AC2KcX5+PkePHiU6OhobG5uOD8jeA+5aAwlfweZnzdbx9K8gYGyLzZUKJTf43cCaE2soryvHzrLzKTErKyvJy8sjNzeXmpoaHB0dcXR0JDAwEDs7u9ZzHJeZE9RfuJDjfCyV5jUwDa4JIQReWltsrVQU6VUEB//hPmgoEFpSUkJqaiplZWXY2dmh0+lwc3Nr886jYYJukG4Qk3s3qwXbdUwmOLIegq4DdesXU09PT6ytrTlw4ACDBw9ukpq0pYm5BrztvNmRuQOTZGoxFWdUVBSLFy/2eeKJJ34UQlwrSZKpWSOZq56rWoiFEAqdTvf9f//7X9+hQ5smNly5P4OvDpxh7ugAnrz+PF9j6Rnzs6MPQItinJOTQ2pqKkOHDsXaugtFM4WAgTPBfzR8fSesvgvu+QF8Wi7KMMF/AquOrWJ75namBDS32lqivLyczMxM8vLysLa2RqfT0b9//85dNPT1flDL1n3TjUJ8XoidEIIAVxtO5jetrXl+gVAwXwzLysrIy8sjNjYWo9GIh4cH3t7enH/nAuYJurK6Mp4b8lzPTgCe2Qfl2dBvYbtNtVotkZGRxMbGMnDgQBwdHdsUYQBvW2/0Jj15VXm427QcSz5z5kzLuLi4yFWrVr0JPNndU5K58riqhdjFxeW/t99++5D77ruvydLl3an5LNiQzPhQHf++4YIJn9Kz5ufzogTOF2M/Pz8yMzMZNmwY3a7W4egDs76DzybAV9Pgbz+De/9mzcJdwvGy9WLTqU1tCnFtbS1nz54lKysLKysrvL29CQ4ORqnsfBwz8IcQtzFJaKU0W7EXxjoHuNqyP73tYihCCBwcHHBwcCAoKIi6ujpycnKIi4tDCIG3tzceHh6klKWw5sQa7g69u+cm6BpIWmc+v+CJHWpub29PdHQ0MTExBAQEkJaW1qoIA3jZegGQVZHVqhADvPnmm3bx8fF/t7e3P1RWVvZ1509E5krmqo0jtrOzuyMkJOSBZcuWNbmXT8+v4OGv4gjS2bJ0+kCUigusq5JMcwJ0a8cmm3U6HTqdjqSkJAYOHNh9EW4cqJvZGra0hZW3QEFzf6IQggl+E9ifvZ/imuJm75eUlHDo0CEOHDiAEIIhQ4YwZMgQvLy8ui7CYC6NBGDReuRDSxYxQG9XG7JLa6is7XhqBUtLS3x9fRkxYgQRERFUV1eza/cu5m2bh5OVU89O0AEY6iD5ewieBJYdv1OwsbGhb9++JCQkEBgY2Gb9QG878wX9bPnZNvtUKpX88MMPTjqd7m0hRMtB2zJXLVelEAshfLVa7XsbNmxwOl+IquoM3P9FLBZKBSvuGYytVQs3BGVZ4ODVLK9CdnY2hYWFDBo0iNjY2KbLobuLYy+zGEsSfDkVSs40azLRfyIGycCvZ34FzLf1OTk57N27l5SUFPz8/Bprt7Xla+0UDRaxqnUhtlCYL0jnh6+B2SIGcx2+rmBjY0NwcDDF3sWcrDrJVMepHEs4RmFh91JUNiF9O1QXQ//bO7VbWVkZR48eZciQIZw8eZKSkpJW23rYeCAQZFVktduvvb09mzdvdnZzc/tBCNEJH5LMlc5VJ8RCCKHT6dZ9+eWXzo6OTa3afWmFpBdU8vpt4fhoW7ndLssCe68mm/Ly8khLS2PIkCF4eno2XQ7dU7gEmd0UtRVmMS7PbfJ2H6c++Dv4s+nUJnJycti1axf5+fkMGDCA6OhonJ2de37xhL4KlFZthtg1uCZqjU0/i971Qnwyv6LLhy+tLWVZ3DIG6Qbx+A2PExQUxKlTp9i3b1+71TY6RNI6851PQMerFJ3vE9bpdERFRREfH095ecsBDyeKTiCEwGDq2J1BYGAgL730ks7Nze29Dg9K5ornqhNiR0fHf9188819Ro8e3UyVYk4XYalUMDLIpfUOynIag/oBioqKSE5OZsiQIY3uiGa5KXoKj3CYuc4switvgao/xEYIwWjdaGLPxXIi6wTR0dGEh4d3bvKts+ir23RLwB+uiYZcEw34OmtQCJpN2HWGt+PepryuvHGCzsnJicGDB9O/f39SU1M5cOAAZWVlXeu8rsq8uKbvVFA1z37aEi1NzNnY2DRO4FVVNU10VFpbylM7n8Jd4869Yfd2eGgPPvigVUBAwE0qlWp0x09I5krmqhJiIYSfg4PD/CVLlrTotDt4uohwb4fGvBDNMOqhIrfRIq6srCQxMZHo6Ohmt/sXTYx9os3hbIWp5gm82nIqKirYv38/QaYgJCTOas42iyq4KOir25yoA3NZJ5VQNXNNWFso8dFqSO+iRXy04ChrU9YyI2RGswk6e3t7hgwZQlBQEElJScTFxXX+f5CyCfSVHXZLtBUdYW9vT0REBDExMY2rDyVJYv7e+eRV57Fo9CIcrBw6PDQhBN98843WxcVlleyi+Gtw1Qhxg0ti5cqVzi1ZidV1RpLOljLYr438shW5gAT2ntTV1RETE8PAgQPRaFoWo4smxgFj4fbPkbITqPxkKvEH99GnTx+mjJxCiDaETac39dyx2qIDFjGYreILXRMAvV2ah7B1BJNk4pX9r+Csdm5zgk6r1TJ8+HDc3d3Zt28fGRkZHfMfSxLEfGKusOLbfq7n9kLUGsYSFBRETEwMJpOJlckr2Z65nScjn6S/a/NImPbo1asXCxYscNXpdO93emeZK46rJnzN0dHxkVtuuSVo1KhRjS6JKn0VXx//Gr1RT06JHuGYRbX6DN8eT8RCaYGFwgKVQtX47FiaTQQg2boTExNDSEgIF/qZL6StRR/dodB1KHnBjxByfCkjHT5GjDYv+JjgN4GlcUs5W362cUb+otEBixjMQtxSqs4AV1t+Ty/EZJJQXBid0gbrU9dzpPAI/x3133YXsAgh8PT0xNXVlePHj7Nv3z7Cw8ObLLhoxtH1kLEXJr/VbgKmjohwA56enlRVVbH+9/W8dfItxvmM4+7Qu9vcpy3mzJljtXLlyslKpXKM0Wjc0eWOZC57rgohFkL4+/r6Pn+hS+JAzgGWxS1r/NvaDdZnmB+tEe7hxrSMZPr539ThZO49KcZGo5Fjx45RXl5OxJT/QwT4wM9PwHcPwq0rmOBvFuItp7cwu//sLh+nQ+irOmYRKyzRm/TNtns4qqnRmyir0eOo6ZgftqSmhKVxS4l0i+RG/xs7PFQLCwv69+9PSUkJ8fHxeHl50bt37+YTmHWV8Mt88IiAQW37bTsjwg24eLvw7sF30VpqeXnEy92aQG1wUURFRa0SQoRIktT1mU+Zy5orXojrV8+tW7VqlfOFLgRDfXmwtTet5ZXvC8ktrWTdP4agN+kxmAzojXr0JvPDYNRzbNOjfKDK4YWcz7hGeZLHXR4n0CmwQ+PoCTGuqKggLi4OLy8vwsLCzD/iqNnmsky/vgSWtnjdtIwI1wg2n978Jwhx91wTFkqzCBlMHQ83Wxa/jIq6ii6voHN0dGTEiBEcO3aMgwcPMmDAgKb/i91LzJEx0z5r0xruigg3+IVLjaU84foE+nI9dPMGycfHh5dfftn1hRde+BCY2b3eZC5XrngfsZOT06O33XZb4MiRI5v9ak31y/ZVQoUCC1QKNQ5WDrioXXC3ccfH3ofejr0J1gYTdu4409JjWWY1gX8N+BdxuXHctuE2Xtj7AucqO5bkvDs+4zNnzhAbG0t4eDgBAQFNRWjk4zDqSYj7An55nol+EzhedJz00vROHaPTdNQibsU10bBYxthBIT5ScIT/pfyPu0Lvoo9Tn86N9fzjKpX069cPPz8/9u3bR35+vvmNonTY9zaET4deQ1rdvysiDPBl8pfsOLuDpwY/xbSR00hKSqKmpqb9HdvhgQcesAwKCpqkVCo7Hmcnc0VxRQuxEEJrY2Pz7KJFi1r8tTQIsUKhoJ+nPam55dQaWqjbWFWEtOlpyuyC8L3pBeZEzGHTrZu4O/Rufkr/icnfTWbpoaWU1bUfKtVZMTaZTCQmJpKfn8/IkSNb90mPmw/Rc+D3d7k+Jw2BYMupLe323y06YRFfGL4GYFEff9wRi9hoMv4xQRfRMyvo3NzcGDZsGCkpKZw8eRJp87OgtITrFrS6T1dFOCEvgaWHljK+13juCrkLtVpNWFgYcXFx3V6AIoTg66+/dnJ1df1ECNGNpZIylytXtBDrdLr/LFy40LG1qIZGIUZBmKcDBpNEyrkW3GxbX4DqIqrHv4adg1kIHa0d+b+o/2PDLRu4zvc6Pj3yKZPWT+KLo1+0W0Ouo2Ks1+s5cOAAGo2GQYMGtZ2vVwiY8DpEzMB191tEaTzZdHpTz60ya3GAHZ+sa8k10WARG4ztJxRbn7aeo4VHeWrwU42pJXsCa2trhg0bBmlbESmbMV3zb7Br2fffVREuqSnh37v+jZuNGwtGLGi8m9HpdDg5OZGSktLt8/Dx8WH69OnOtra293W7M5nLjitWiIUQ3nZ2drfNmjWr1aQPDUKsFEr6eZl/WEeyS5s2OrYB4leS2/sO3CLGN+vDy9aL/476L2tuWkOYcxiLYhdx03c3seHkhsb+W6I9Ma6oqGDv3r34+fkRFBTUMX+oQgFT3oXQm5hw5jCnSk+RUtz9H3mrGDpoESssm8URA6g66CMurilmWdwyBrsNZpL/pK6NtQ0UJj29Tyynzt6P/dIA6uqaj7WrImySTMzbO4/C6kIWj1ncLE9ycHAweXl5FBc3zxHSWV588UU7GxubBUKILqT8k7mcuWKF2N3dfemSJUu0bSW1aRBKIQQ+ThrsrFQcbRDiM/vh88nw7UwqNd443/ZGm8cL0Ybw0XUfsfy65ThYOfDcnue4Y8Md7M3a26pV2poYl5SUEBMTw4ABA1qv6tEaShXc9gnjXQejkiQ2xixrf5+u0k3XhKreNdGej3hZXPcm6Npl//uIopNYTllM76AQ9u3bZy7zVE9XRRjgi6NfsOvsLp4a/BRhzmHN3lcoFAwcOJDExEQMho4nQGoJJycn/vnPfzo4OTk90a2OZC47rkghFkKEurm5jbnpppvaHP/5FqtCIejraU/N6VhYeSt8egNS/glOhcyl+p5fsNB0bOXTMM9hrJ68mtdHvU6FvoK5v87lga0PcLTwaIvtLxTjoqIiEhISiI6ObjdGuVVUVjhN/4aRkjXfZe2kMvdI1/ppC0mqn6zrCddE60J8ougE61PXc3fo3QQ5BXV9vK1Rlg0734TgGyFwPO7u7oSHh3PgwAGqqqq6JcLxefEsi1vGdb7XMSNkRqvtbG1t8fX15fjxzlfyvpAnnnhCo1arHxVCdHypnsxlzxUpxO7u7h+89957zu1ZT772voC54CTZ8bxc9SqLSh5Dyo6H617m7K0bKAu9Cxd3rzb7uRCFUDCp9yR+vPlHno56mhNFJ5j+03T+b9f/kVme2ax9gxjv2bOHxMREhgwZ0v0cEZY2zBn7OsVKBV//NNu8PLsnaajK3B3XRIMQm1p34aw6tgprlTVzwud0bZztsfUFMBnghlcbN2m1WiIiIvj99985ePBgl0S4uKaYf+/8N562niwYvqBdS97Pz4/S0tJuJyvSaDTMnz/f0dXVtfUZR5krjitOiIUQQ0NCQvqNGDGi3bbhTsHYKa3Yu/15WD4G/6pE3tTfQdpd+6iJfJC0Mzn07du3y2OxVFoys+9MNt66kQf6P8D2M9uZ8v0UXjv4GkU1TX9wQohGF0arpYk6SX+/axnt0IfPRTnl21/pkT4buSApvMlkoqamprG4qNFopLKyktra2lbD19rzERfVFLExfSNTAqZ0KhdDh8nYZy7YOuLRZnUBlUolkiQhhOi0O8QkmXhuz3MU1RSxaPSiDpWvEkIQERFBUlISpjYuTB3h/vvvt7SxsblbCNFJv5bM5YrypZdeutRj6DBCCOHm5vbT6tWr/RsWULRIaRbsexvFd3M5KlUTYyG4Z+gzZF6zmIcPOKK1t8WmMgt/f38cHLovAFZKK4Z4DGFqwFTK68pZm7KWNSfWYJJMhGpDqSyvJCkpiREjRmBvb09CQgIeHh7drmoM4O8azqq0/2F1Zj9RnsOaVBbpLAaDgeLiYnJycsg9lYxr2hpOKPpwpFDZWHapsLCQ/Px8ysrKqKysJCsri/25+zlbfZaAogDOnTtHcXExVVVVnCvX8/PRfKZFeuPl2Nyy/vLol/ye8zv/GfUfnKzbKb7aWUxGWH23OVxt2qeg/GNOt8EdERUVhZeXF3Fxcbi5uXU42f+nRz5lTcoano1+lrG9Wq412BKWlpbU1dVRXFyMs7Nzp0+pAYVCgbe3t9WuXbu8nnrqqfVd7kjmsuGKsohVKtXEkSNH9urXr1/LDTL2wbezYGl/2LUIvAYzKuI+8hSQGjIef29PJvV3Z/muk+SV1XR4CXNHcbNx46XhL/HdlO+Ido/mnfh3uHH9jby3+z0GRg7EysqqxxMFhTqHMt57NF86OlD63QNQU9r+TvUYjUby8vJISkpi586d7Nu3j7Nnz6JSqXB3Mfuv+/QbwJgxY7jmmmsYNmwYUVFRjZWMo6OjGT58OL28eiFUgtGjRxMREdH4uRbkmXMqx8UncuyYOal7gzWoN+r59sS3jPAcQW+H3t3+HJpx6DPITYIbXmlSc+9Cn7C9vT39+/dvkjmtLeJy43gn/h2u972eO4Pv7PSwAgICyMrKajJZ2BVuu+02pbOz8/VCiI4t/ZS5rLliljjXW8NLFy9e3LLpdHAFbHzKXIl3+D9h8H3g5MfwylxIW82erD30cerDv68PZsuRc/yWa82EizFDD/R27M3b497mwNkDvLrnVVYXrSZ2WyyLRi8iwDGgxxMFPTToEX47u4svKOWRjf8Ht37Ualuj0Uhubi6ZmZlUV1fj7OyMm5sbffv2bVpWKccs6KIDk3VWSivqjHUIIVCr1ajValxdXSkUDrD9d/qEhOLgYCIzM5PDhw/j4ODACcUJ8qvzWTD8Irg6q4pg2yvgNwr63ty4ubWJOWdnZwIDAzl48CBDhw5ttbxUekk6T+18qplfuKCilsNnSzh8tpSks6UcziqluLIOlVJgoVBgoVKgUggslApUSoFCMmH6fRf2tjZYqhSEezswJcKTAT6OHXaTCCF4++23nWfNmrUU6MGy1jKXgitGiIGRw4YNc/b19W3+TtxKswgH3wjTPmkyweRm40Yfpz7szdrLff3uQ1FVyI3BdvwvIYc5Y8oJcut8efqOYDQaqTtVx4qxKzhSc4SF+xcy4+cZvDziZSb4TehRMe7j1Icb/G5gVcavzDyyBm3QddB/WpM25eXlpKenU1RU1GiVtzlB1egj7v4SZxQKPD3d8fT0RJIkioqKWLBtATqVDqdSJ6qdq3s2v/K2hVBTBpPebCx51V50hKenJ7W1tSQkJDBo0KBmghh7LpZHtj+CSlhwb++X+GLvObPoni0hu9Q8sSkEBLraMirIBXd7awwmiTqDCYPJhMEooTdKGEwm9EYTeQVFWFsJ9JLgq/1n+GzvaXy0am4K9+SmCE9C3O3aFeVx48YJBweHaCGEhyRJOT306clcAq4YIfb09Hz5+eefb55MOGkd/PgvCLgWbv8MVM0FbYTXCFYmr6S0upT09HTm3RzN9rf28Nqm43zyt6iLMt4jR47g5eWFm5sbbrjR37U/T+18in/v/DeH8w/zeOTjPSrGDw14iF8yfuEz7z48+dMT4DMEycGbgoIC8/JeSaJ3796Eh4d3zOpqKO3TTppIAAulBUbJiNFkRHle+4Y44vPD14QQZBozSa9K55moZ3CwcyAmJgYbGxsCAwO777PPSYTYz2DIXNCFAh2PE/b396esrIz09HQCAgIAOF1Qyfsx69ictxRh0FJ2+m88nZAP5OPnrCHST8vfvRwI93YgzMuh5TqILVBeXk5iYiIjRgylvNbAL0dz+TExm492nuT9HScR5bmoshK4e1QILz3ZdMm3JEk8+uijbNy4kZqaGhd7e/s3gFld+rxkLguuCCEWQviGh4eHRUZGNn3j2AZYPwf8RsKdq1oUYYBRXqP47Mhn/JjwI8N7DcfN0YZ/jA3k9c3H+f1kIcMCuj5x0hJnzpzBYDDg7//HTL1Oo+OTGz5hcexiViav5GjBURaPWdxjYtzboTc3+t/I6tNbuFeYcFg7m4Ohz2OtNlcc7mx4Fup6D1B1+yvCGurW1ZnqUCv+sGzr6pc2qy7IRfzVsa+ws7DjlqBb0Fho8Pb2prCwkOTkZCwsLAgJCcHWtgvLnCUJNv4faJxhzDNA5xdr9OvXjx2797IvS8+GY0XEl/6AtdtGlLX+RFo/yaBxXkR4O9LfywEHTdcredvZ2WFnZ0dOTg6enp5Mi/RmWqQ3ySfP8MOhDOKLtcTYufF5PmQs38Hy2ddgoTRf2DZt2kRqaiqpqans3r1bjB8//k4hxAOSJHU/w5DMJeGKmKxzc3N7Zt68eU3VMnUrrP07eEXCjG+aTMhcSGF1IQB5hXn4+fkB8PcRfng6WPOfjccwdSJNY3uUlJRw6tQpIiIimlmeFgoLnol+htdHvc6xomPcseEO4nLjemwCb27EXPSSkSW9orHIOkBkzb4uxcgCZjEDqCpst6mlwpxr+EL3RH65WRdc7f64uJyrPMfWjK2NIgxmK9nFxYVhw4bh6+tLfHw8iYmJLS5FbpPDayBzP4x/CdSOnRbhI1mlvLghmce2VzN/YyrpxlVYu21klOc4Dsxeyyf3jObhsYGMDHLplgg30KdPH1JTU5uszOwb0Itn7xjFmgeHse/ZcegK4tmeXsnclYeo0ZsTVv3www/cc889CCG45pprsLW1VVpbWz/c7QHJXDIueyEWQqhVKtWtt956a9Ox/rbAHKp191qwat3PW6mv5M2YN/HX+HNz2M2NEzHWFkqeuiGYpKxSNhzO7pGxGgwGEhISiIyMbDM0bVLvSXw16Ss0Fhpmb5nNquRVuLq6dkuMTSYTdXl1RGmi2Gw8zbnQiVjvexOy47t2Mpp6L1BV+wsQGgqIXijEuWXm83Cz/yM1wrcnvkVCanUlmqurKyNHjsTZ2Zm9e/dy9uzZjiU2qi03L97wHAQD7u6wCJdW6fli32kmLdvN5Hf2sDb2LGNCHBg65AdqbXYzK3QW745/q9Hq70nUajVarZbs7Ja/f7XFuZz7ZTnzJ+cJSCUAACAASURBVASy7UQef/8shopaA1lZWfj4+DS2CwsLU2g0msd6fIAyfxqXvRBbW1vfec8999g0EzZtb3OsqLrtZcIfJn5IXnUet9jdgr9v06D+mwd40dfDnjc2n2g5PWYnOXr0KP7+/h26rQ5yCuKbG79hlPcoXo95nad3PY2tk22XxLi8vJw9e/ZgMBiYf918JCQ+9goEGx387wFzxeLOorQAa4eOWcT1QnzhMue88hqUCoGzjfn9GkMN61LWMdZnbJtlnoQQeHt7M2LECAoKCjhw4ED7eX23vggV52DSm5RVVLQpwiaTxL6TBTy6Op6o//zKiz8eRQh4eWoYW56MpMjhHZLLDnKP9z1Mc5mGQly8n0lQUBBpaWnNLjYVFRXcdtttLF26lNljgll65wAOni7i7o8PYLjgomBpaUlQUJCtEOIC353MlcJlL8ROTk5PzZ07t/l6YN+RUHoGiluve5RWnMaq5FWM141ndJ/RzVa0KRSC5yaFklVSzTu/pXVrnPn5+VRXV9OrV68O72NnacfSsUt5dNCjbMnYwt0b76bKqqrDYixJEhkZGRw6dIiIiP9n77zDorq29/85U+gMvYN0AQFRBEXFEkuixNgSjbHHknJTNN6Y5MbExGhibupNosYUE40ppmmKmmgUUVGxoGJDFAUpIr33mdm/P46ghCIg3Ov3+fE+zzzozNl79oGZ96yz9rveFYK/vz/dLLox0WciP6ds4+roNyA/GXYuad9JmdhAed4tD6uLhOsIuQ7ZJdXYmRnW96vbdnkbRdVFre7jZmBgQK9evfD09OTQoUPk5OQ0fWDCJji2DgY8RYmme7MknF1Sxeo9yQx9J4apnx0m+nwOU8Ld2PpUJNueHsTQQAVP7HmYpIIk3hv6HouGLiItLY3y8rY3QG0tjIyMsLS0JDs7u/652tpa7r//fqZNm8bEiRMBGNfLhbXT+5CYVUKG7wOcu5xRf3xGRgYLFy60dHJyeq7TFtqFTsUdTcSSJPl7enraN0luHpHyz9TYJscWVRWxPG45JmoThqmHNUuQkb62PNDHlVV7kvnhWGOfiNagtraWM2fONJkXvhUUkoJ5wfNYO2It+ZX5TNk2hdOVp29JxjqdjuPHj1NQUEBkZGQDtcH8nvNRoOCTopOypvrYF3B+e9tPzMSmVRFxXTm3lWFDiXdOaTX2Gjl6E0LwdeLX+Fn5EeYQ1qZl1Bm8X7p0ifPnzzeMHq+dht8XgscgSvouapKEiytqeX3bOQb9ew9v70jCxdKY/zzYi6NLRvDauCCCXCw4lXuK6dunU1JTwud3f84I9xEolUp69uzJyZMnO9X32cfHh+RkORAQQjB37lwCAgJYtKihydrIHg58OTucGgMN/zlcjBCCuLg4LCwsmDx5MiqV6i5JkjrOzLkL/zXc0UTs4OCw6Nlnn21a0mDnLxPFTUQshODYtWO8sP8Fhv84nOM5x5ntORtfV98Wc7ZvTAhmkK8t/9p8mpikZqKuFnDu3Dm8vb1vSwvb37k/34/5Hk+NJwtjFvJN+jd09+veJBlXVVVx6NAhbGxs6N27d6NzczR1ZJLfJH5N/pW08NngGAy/PQml2bQJrSTiwqpCzNXmqJUNN7BySqqwN5fzw4evHSa5KJlpAdPaZXVpZGREREQEOp2OY8eOyZaSlYXw/XQwtqL0ng+IP5HQgIRrtHrWxaYw+O09fB6bwrhezsQ8O5TvHolgfG8XjNTyfkF0WjRzd8zFVG3KxtEb6WXfq/59ra2tsbS0JCUlpc1rbi1MTU0xMjKioKCAAwcOsHHjRqKjo+nVqxe9evVi+/btrF27lrVr1zLQx5YFI7tTYe6Kd0g/5s+fz5o1a1AoFMydO9fUxMRkaqcttAudByHEHfkAlI6OjtdqampEs9g0XYj3gkRBZYFYf2a9GLN5jAhaHyQivokQKw6tEIl5iWLv3r2isrKy+Tmuo7SqVoz+zz4R8PIf4lR60S2Pr0NRUZGIjY0Ver2+1WNaQrW2Wiw7uEwErQ8Sc/+cK5LSkkRMTIyoqqoSQghRUlIi9uzZI3JyclqcJ6c8R/TZ2Ee8uP9FIXLOC7HcXoiNE4Voyzq3PC7Euz2afGnPnj31/14cs1hE/RzV6Jjer+0UL24+JYQQ4sldT4rBmwaLKm1V69+/GaSmpop9e2OE9qv7hVhmI8oSo0V0dLQoLi4WQgih1+vF9lNXxeC3ooX781vF9M/jxNnM4ibn+i7xO9FzQ08x5fcpIq8ir8ljamtrRXR0tKiurm702sMPPyzs7OxEYGBgk2P37NkjNBqNCAkJESEhIWLZsmVNHpefny+OHTvWmtMXmYUVwuOFreK9nUkNn8/MFE5OTmfFHfD97Xq07XEnR8T9hgwZomrOiEUIwRE7T54zKGf4j8N459g7WBpasmLgCqInR7MkYgl22NVHG7eCmaGK9Q+HY2ViwMPrj5JecOsNLiEEZ86cudFxuQNgoDRgaf+lLB+4nJO5J/lH3D+QnCTi4uLIy8vj2LFjhIaGYmdn1+I8diZ2TPGbwtbLW7lsoIa7V0DyLjjyaesXY2IDFXmyPrcFFFQXYG3UsNamRqunoLwGe3Mj0kvS2Zuxlwe6P9Ah6gN3d3d6l+1GeekvSiOXcCSL+kj4eFohD6w9xOPfHMdIpWT9w+F8NacvPZwb5ov1Qs/78e/z+uHXGewymHX3rMPGuOmbL5VKha+vb5N+wrNnz+bPP/9scb2DBg3i5MmTnDx5kqVLlzZ5jJWVFeXl5a1qNupsacwAbxs2n2ioKHF2dsba2tpOkqSWPxxduONwxxKxg4PDtKlTpzb5zRBC8Prh15mbvoVYY2MmWwazeexmNkZtZJzPOIxVcoogNTW1QVHFrWCvMWLDnHBqdXpmfXGEgvKWdaxZWVmYmpq23+C9BYz3Gc/G0RtRKVQsPLyQM6ozHDp0iJCQkFbrgucEz8FQacjak2shfB743g07X4acxNYtwsRG9iWubfmiVFhV2Mg9LbesTrpmyLfnv0UpKdtlktMkLu7C7MiHlHmPIabMm8DAQIpqVTzx7XEmrjlIWkEFb04MZvuCQQz1s290kazR1fDC/hf44swXPOj3IO/f9X69prk5uLi4UFJSQklJwwaygwcPxtq6ccFnWyFJEu7u7ly50vzm8824P9SV9IJKjqY2LLiZMmWKmYGBQZf3xP8x3LFELEnSmBEjGveQA1h3Zh3fJ33PdP/pRFea8ULCTnyzLzY4pqamhtLSUqys2mav6GNvzrpZYWQUVTJvw1Eqa5qWtel0Oi5cuIC/v3+b5m8LAmwC+H7M94TZhbE2eS27DXYTnxDfammbtZE10wKm8Wfqn1wsSoZxq2XN9c/zQNuKOVpZ1FFYVdgoIs4ukSM7jYmOLclbuMfzHuxNWrAubS0KU+HnuejsAoh3moFXQDBLN59k+HsxRCfmsGC4LzHPDmVK3243vC5uQklNCY/teow/Uv5gQegClvRbgkpx6wJTSZIICgrizJm2d0Opu4COHj2as2eb7uQCMtlnZWU1iHKbw6ggR0wMlPwcn9Hg+YkTJxrb29vPbvMiu/A/xR1JxJIk+fj4+Bg31Z3590u/88HxD7jX614W912M0aytYO8P30+TPQauIzMzE1dX13alDMI8rPlwSi9OpBfx9KYTTfZcS09Px9HRsVVpj9uBgd6AKYZTmOM/h+hr0awpXMPW/VtbTcazA2djqjZlzck1YGYvk3H2Gdj92q0Ht4KIhRAUVjeOiHOuE/G50t2U15YzPWB6q9bbImor4YeZCCE46P4kZ3Bn6rcX2ZFaywBnFbueieSZkd0xbcbvIassi5nbZ3Ii5wRvDnqTecHz2vT5sLS0xMDAgPz8W29g1iE0NJQrV66QkJDAU089xfjx45s9VqVSYWFh0ar5TQxUjA5yYtvprAafz4CAAIAASZI6vgKlC52GO5KILSwsHpg+fXqjUPbg1YMsPbCUfo79WD5guSy0N7ODWVtl05+tC2HPGyAEGRkZDaqP2opRQU68el8gf53L5pXfzjSIUvR6PSkpKXh5dYKP7k3QarUcPXqUkJ4hPNPvGVYNX0V2dTbvZL/Duuh1rSJjC0MLZvSYwa60XSTmJ4LfKOgzG+LWQM4teqjVEXF588RQWluKVq9tUroGev7K/JkQuxCCbJvxkG4thIBtz0JWAn86PcGLZx15e9dlQtws2b5gEMvv8yfj4tlmo8nzBeeZtn0aORU5fDLiE+71urddy+jevTtJSUmtPl6j0dQX+ERFRVFbW0teXvPa7G7dupGWltaqub3sTCmr1jZoRSVJElFRUWpgaKsX2YX/Oe5IIjY1NZ06duzYBmHN+YLzLIpZhKelJ+/f9X5DqZShmew30Xs67P03tZsfR6WQbtvnd9YADx4d4sXXcWmsiblU/3xGRgYODg4YGBi0MPr2IITg5MmTeHh41HdzGOw6mO/HfI+rxpWPcz7m5T9epqLy1puK03tMx9zAXI6KAYYtBQNz+Ovllgea2so/W4iICyqva4j/FhFnl1RhYJ7E1fKMjomG49fDya/5w/wBnkgKQpIUbJjTl6/m9CXASUO3bt0wMzPjwoULjYYezDzIrD9moVQo2TB6A32d+rZ7GRqNBqVS2erec9euXau/OBw5cgS9Xt9idw5ra2uKi4vR6dpf6TllyhRLZ2fnWe2eoAv/ddxxRCxJkpVGo3G8uc18ta6aJ3Y9gbHKmDXD1zTdI0yphrGrYPBzqE9/R6/EN6Hm9iuinr/Hn/G9nHl7RxIrtyei1ekb2CR2Fi5fvoxarW5UiOJm7sbG0RsZ6z2WP4r/4OHfHyanpGXts8ZAw+zA2cRkxHA69zSY2sDgf8LFnXBpT/MD6/0mmifiwmp5s+jvOeKMwkpM7A5hb2LPcPfhLa7vlsiIR799MUcUITyRO57xvV3Y9nQkQ7o3FAcEBASQn5/foALvl+RfeGL3E7iau/L16K87pFO0n58fFy/KexIPPfQQ/fv3JykpCVdXV9atW1ev+QX46aefCAoKIiQkhKeffppNmzbdSIfodbKXR/4lyIiHi7uQTv9E94qj5F88cku1SnOIjIxEp9PdJXWUlKcLnY47zgZTrVZHTZ48uUFJs1JS4mDqQGJ+IsezjxPlFdX0YEmCYUu4mF2Gz4W1sH6MbApUF9m1AwqFxNuTQjA3UvPJvsucTM1lQV/L2462W0JRURFXr15lwIABTb5upDJixcAVhNiF8ObhN5n8+2Q+GPYBIU4hzc45LWAaG89tZPXJ1awduRb6PgpHP4edL8Gj+5r2HTa0AEnZckRc1XREfCIrEZ31BR7yX4BacRtOZeV5lH/9EIU6SxbyNO9PCWVcr6a7bisUCvr06cPBgwcxNzdnfdJ61iSsob9Tf94b+h5mBh1TdGZpaYler6e0tJTvvvtOJsyKfJlUKwtvPA6t4ckexTz51ugbz51ZAkev/7uqGGhMti4ARwErDznl5jMcPAe3aG51M9RqNWFhYapt27aFACc75KS70Km444jY3t7+4fvvv7/BLp1KoeLTkZ/yVPRTvLD/Bcpqy5jsN7nJ8RUVFeS634dv70j4aQ6sGwnTf5ZNgtoJtVLB8vFBBDpreOmX0zxXUsvnriX4O7bDXvIW0Ol0JCQkEBoa2mzLHpBzgZP9JhNgHcCC6AXM3jmbF/u+yKSASU0eb6o2ZU7QHN6Lf48TOSfobd9btov8aQ6c/BZCm/AVVyjkqLgiHyEEWq0WrVZLbW0tOp2OyspK8q+T9M0RcUlVLdnSbowlAx7wfaDxvK1EWWU1masewL2ygHct3+L7WVG4WbcsMzM0NKS7f3cW7VhEbHEsY73H8uqAV+svBnPmzGHr1q3Y29s3qYAQ4obpuomJCevXryc0NLTRcd42aopi1mCuTZGrO4ubK4+XZGMqYyv5YWINNt43/m9002vXH0LoubBzHd0VaUh1PhoKFbhFgM8wmZwde970Do0D32nTptnExcVNoYuI/09Aao1U5r8FSZKULi4uV9PT0+2buquq0lbx7N5n2Zuxl4WhC5kbPLfRMZcvXwaQN9LSj8C3k+UP8dQfwKXxF6otKC8v58foY6w5VUtZtZZ3JoUQFdyxHc3PnTuHgYEBPj6t7wlZUFXAwl0LOZF/ggneE3ip/0uNDHgAKrWVjP55NN6W3qy7Z50cya0bCUVp8NRxOdd+HRUVFeTm5mL/01jKjJw4G/gCKpUKtVqNSqUiOzsba2trfs/5nd8Kf+NDzw+xtrDGxsaGhIJyno+fwkDHu/lk9L/b9Xs4mV7E6Q3PMEO7ma0eLzJqxmJUyltn0spry/lnzD85cPUAUz2m8sLgFxooI/bt24eZmRkzZ85skoi3b9/ORx99xPbt2zl8+DALFizg8OHDcmfw1P3yI2U/FMl6X2Fig+QRCW79wMyhIekaW8l3FYq2ZwATEhJwdnbGzsoC0g/LxTiXdsveGgCmdiSZhrM6w5N3Xl2GgUHDu46ioiJ69Ohx8erVq93b/OZd+O/jf13ad/MD6DF69OgWa3drdDVi8d7FImh9kHj/2PuNSosPHjwoysvLbzyRe0GI94KEWOEkxIW/Wpr6ljh79qzIyMgQ14orxYTVscL9+a3irT8ThVbXMeXNxcXFYt++fe0ql67V1YrX970ugtYHiRnbZojS6tImj/vq7FciaH2QOHz1sPxE2mEhXtEIEf26qKysFElJSWLPnj3i4MGDIjk5WdR+erfQrxvVaJ66Euc3D78p+n7dV9TU1Ii8vDxx/vx5cf/6F0TQ+iDx27G/RIsl6k1Aq9OL1XsuikdffFWIVzQiY8PcVo/NKc8Rk36bJEI2hIgfEn9otiw5JSWl2ZLkRx55RHz77bdClGQJcepHsWmag6h9N1j+Hb2iEWJlNyG+myrEoY/F5UO/i7QrqW06v9bi2rVr4vTp041fKLkmxMnvhPhprihf3k2IVzRCu/uNJufw8vLKAQzFHfDd7nq0/LijNuskSeozePDgFu/31Qo1KyNXMrn7ZNadWceKuBXohSzf0el0VFdX00B/bOsL8/4CGy/47kFZ3taGlvN10Ov1ZGdn4+TkhIPGiO8eiWBKuBur91xi7oajFFfeuhV7SxBCcPbsWYKCgtqlfVYpVLw46EWWhCwhITeB+TvnU1JT0ui4yX6TsTe2Z/XJ1fLFz60vtd3vQ7f/PyTs/wNDQ0MGDhxI//798fb2RqWxR6psXiFQpyFWq9XY2Njg5etFCgdRVncnwMKDAwcOcOrUqVa1j88qrmT654f5cUcM76k/psa+Jy5TV7fq/A9kHuDBrQ9ypeQKq4avYpL/JLy9vVsvNSvLhTObGaeMYVz6CnjXD36ey70eNZQZO8M9b8Cj++G5FJjyDUQ8hmPIcK6ktc+x71awtbVtWk9s7gAhU+D+z1ng+gMHVH1RHvlYbpb6N/Tu3VsCgjtlgV3oUNxRROzs7DyiX79+t9wFUyqUvBTxEnOC5vDDhR/41/5/UauvpaCgoOlyU3NHmL0dAsbC3n/DByEQ+36bVBV5eXnY2NjUexobqpSsnBjMivFBxF7MY/zqA1zMLm39yf4N2dnZGBoatrkS8O+Y0msKr4a+yvn888z5cw6FVQ1LYA2VhszvOZ/jOcfZe2Uv8fHxJNhPQIGgX/lfuLu708Df4xYObH+vqtt9ZTc1FOBvEoWPjw9DhgzB1taWI0eOcObMGdk1rQnsOpfN6A/2cyE9i+/N/4ORsTEGU79ttg9hHSpqK1gRt4LHdj2GxkDDV6O/ItJFtkh1c3OjqKiI0tLGfxdLAx2c+1XWJq+OgHd84KeHGWqTS5WxI4x8DebvYcKhXiSHr4D+T4BTzwZpBmNjYxQKRasuMm2FUqlEpVI16z0hhOBERimH3ebJgcXRzxodM2TIEEu1Wt02z9Eu/E9wRxGxXq/v27t371YdK0kSz/R5hgWhC9iesp1n9jxDZnZm82Y4Rhq5y/MjMeAaDrtelQk57mOovbXRytWrV3F2dm60hukR7nz3SASlVVrGrz7AjrPXWrX+myGEICkpqa4q6rYxIXgCy8OWc7noMg//+TB5lQ0LCCb4TMDO0I63Dr2Fo7MjfYZPRIp4VN60yzrVcLI6ItY3rWv9u8/E+jMb0dfYMNR1MCD/jpydnet6qxEbG9vI4H3DwVTmbzyGk7kBm20/w642E8WkL8Gy5YKchNwEJm+dzA9JPzCzx0y+v+97/Kz96l+XJIkePXrIZj3VpXB+G/zxAs6/TiJ27FX4YSac/AY0TjD8FZi3m3/m3M8O23kwcAG4hJKWkYmLS9MqDQAnJ6dmWx3dLuzs7MjNzW3ytavFVeSVVWPbvR/4jIRDqxsFFuHh4SoHB4fb1A524b+BO4aIJUlSqlQq67Ya6MwLnsdL/V5iX8Y+lp9djpHmFiXHzr1lSducnXK79T9fgI9C5fJoXdPpBSEEhYWFzQrxwz2s+f2pgfjYm/Hoxnje++tCmxqSZmVlYWVldVt+xn/HmMAxrAxfSXpJOrP/mE12uexFrNVqOX3yNJMcJpFek86ewj1yKmTQs/Lm0s4lDfWrVh4g9LLHQxMoqCqor6pLLkzmbMEpagojCHFreGciSRIeHh7069ePy5cvc+7cOXQ6PW/+cZ5XfjvLEB9rPtJ8g3vhAaRhL4PX0GbPrVZfy0cnPmLmHzOp0dWw7p51LA5f3NjZTQhsypPpdvItxDvdYdNUiP8SnZElH57RwJwd8PwVmLEFBi0C1zDGjB3PV199hRA3TNdv1rT/HU5OTmRlZTX7+s3Q6rWkFqdyPPs4l4oukV+Zj1bf9B0CgI2NTbOFIwnpRQCEuFrC4MXyxfKmEn+Anj17otVqb2+Hugv/FdxJ8rXu7Y0IH/R/EFO1KUtil/DQnw/xQPcHGOc9DjuTFtwAu/WDWb/D5b0QvUIujz7wHxjyAvSc3EBXm5+fj7W1dYu5WycLY75/tD9Ltpzhw90Xib2YW9/9oSUIIUhOTiY8PLzN530r3BNwD2qFmucPP8+sP2axeshqMhMz8fDw4LE+j3Fq9yk+PPEhw7sNx8nMSW5B/8dzcGGHXAoNYN9D/pmTKMuu/rb2m1MTO6/sBCR0Jb0Icmk61W9sbEy/fv04c+48sz7eTWxGDZN6O/JI5Zf4pP4gV0dGPtPsOV0qusS/9v+LxIJExnmP4/m+zzcu8CnPk9snHf8K8pKwV5uQ7zgE22H/YMaSVezas5+8vDzeinuAZcuWUVsrX4Afe+wxoqKi2L59Oz4+PpiYmPDll182sYobqPMaqaqqqv93aU0pqcWppJSkkFJ845FWmtYk8WoMNFgaWmJpZImVoRWWhpZYGVlhYWBBbloueVZ58vPXX9cYaEhIL8JAqcDfyRxU/cBjEBz8EMLnglq+oJuYmGBkZGQuSZKBEKKNLbG78N/EHSNfUygU01esWPHZiy++2C4XnYKCArad2cau8l0czzmOUlIyyGUQE30nMsh1UMsOW0LAxb8gejlcOwW23eGuFyFgHCgUnD59GgcHB+ztb+0eJoTg5+OZrNyeSGFFDdMj3PnnSL9m26/n5uaSkZFBa1My7cG+C/t4Nu5ZDBWGrB6ymp5usgY1syyTCb9OINwxnFXDViHptbAmAiQFPH5QrlasLoOVLnDXSzBkcf2cMTExhA8MJ+LbCBb1WcTDQQ8z/pfx5BSrMM57kt3/HNrsekqqann863gOJOdzv6+aR9R/4nd5HQQ9ABM/bXAR/PPPP1mwYAE6nY7IpyM5bXUaU7Upr/R/heHuw1m/fj2LFy/G1cWZCLtKFo9wxKv6HOhrwSUMQmciAicQezSBsLCwDrvr0As92eXZpBSncPTyUTKrMsnX55NSnEJu5Y10gkpS4aZxw1PjiaeF/LA1tqWkpoSi6iKKqooorC688bO6iMIq+effm7HWQUJCIUxQCDOCHJ2ZFzyPwQXXYPN82XfFc1D9sRMnTszbsmXLPUKI4x1y4l3oFNwxEbGTk9Pwfv36tdvKrKioiEHdBjHDYwapxalsSd7Cb5d+IyYjBltjW8Z6j2WCzwQ8LDwaD5Yk6H43+I6ExN9hz+vw42xwCIZhSyjIN6ZHjx6tWockSTzQx5WRAQ6891cSG+OusO1UFi+M9uf+UNf6Rpp1uHLlSqeXS4e5hvEP23+wNn8tCw4uYN096/Cy9MLFzIUnez3J28feZkfqDkZ5jpI3qTZNlb0d+s6XtcVWHpDT2L7x5qq65MJkLhVfQl14PxGuzaeXskuqmPXFEZJzylg+pjuhKZ/jd2kder97UUxY24CEdTodTzzxBN/+/i1rr6zlWM4x+mj68M7d72BrLFdLmmoLWD/bn3udi6A4G6iR1917BjjIfzMJ2Uw+LS0NPz+/JlbVPKq0VVwpudIguk0tTiW1JJVK7Y1NOmOFMb42vgxwHlBPuJ4Wnriau7a7srBSW0lcQhwGFgZIxlI9UedVFPBJ7Gnc7QTZ5Wm8fOBltqt8MTXUNNLKDxkyxGLr1q3hQBcR38G4Y4hYCNGvqQqm1qK4uBgPDw8APCw8eKbPMzzZ+0n2Z+xny8UtbDi7gS/OfEGofSgTfScy0n1kYzNwSYIeY8H/XjizGWLegO+m0Fvjh9Lt33LespXSMgsTNcvGBTEpzI2lv55h8U+n2HQ0ndfGBRLoLKcrqqurqaio6BRj+TrU1tZy9OhRxvUfR4+CHjxz6Blm/zmbz+7+DD9rP6YFTGN7ynZWHllJf+f+WPhFyR2yY1bKKRojCzk90YSZfJ0iw9rImp1XdiIhUZjrT0jfps/nYnYps744QnFlLasmB9Lt/JcEXPqEKrdBJLg/Rl+FqkGN2OHDh3Ee6czCkwvRCz39ivrhddUL23s1suLh+Fc8kLEbyVSAzV0w8lXwH9Ok0sLFxYV9+/bh6+vbqJu3EIKCqgKZaP+WTrhadhVxvQxZQsLZzBkPUDXsaAAAIABJREFUCw/6OPS5QbgaTxIOJTBs2LAO69QCYKwyxtvOm5qaGnxcbhT4xCTlUJHlxXOjwrGzyeGhbQ/xRXE0TwU/AAYNG56Hh4er7e3thwOfdNjCutDhuCNSE5IkKVxdXa+lp6e3u8XL3r17iYyMbLYsOLcil18v/cqWi1tIK03DVG1KlGcUE30nEmjTTKsjXS1Fez/G9Nhq1BXXZIIa9hK492/T2vR6wc/HM3jzj/MUVtQwI8KdRXf7kXc1DYVC0aYuIm2BEIKjR4/i7OyMq6srAPEp8Sw8sBChFHxy9ycE2gSSVJDEg1sfZKz3WF4b+BpcPQGfDoWBC2HkMtm7+MAH8OLVepKLiYlB8pZ4MvpJvo36lpcPvExVtTHnT0xn3+K76GbT8CJ3JKWAeRuOYqhWsmpSD0xPfklg4rtI7gNg2o8kJqcihKi/8yisKuTRnx4lUZdIqH0oKyJXcPyHTZgmbWaEbY7cwsncmZOKYB75eC9VRg50796d999/v1n701OnTmFqbUqGyOBS8aUGhHuz5tpIaYSnhSceFh71ROtp4Uk3Tbf67i9/x5EjRwgICMDcvHV+EK1FSUkJFy5cICzshgpt6a9n+PFYBieWjsRIreS5Lfezp+g8W4d8hIPXsAbjKyoq8Pb2vpSVldX6Us0u/Ndxp0TEzt26ddPf+rCmUVed0pI3g52JHfOC5zE3aC7x2fFsSd7C75d+58cLP+Jr5ctEn4mM8RqDpdFN0ZxSTbrdXTjOnIhd2h+w7234chT4jIC7lrS6ZFqhkJgU5sbdPRx5ty5dcTqLid5KnhnftLFPR+Dy5cuYmJjUkzBAH88+rJJWseDAAubumMvaEWvpZd+LWYGz+OLMF4zxGkNf577Qc4rsWRw2R46I9VrITwaHwPq56lIThdWFXCq+hLN2Kr72Zo1I+I/TWSz4/iSuVsasntSD2iMbCDz/HpJrODy0CdTG+Pv7c/jwYXJycjhfc56lB5ZSpCvCI8WFL4JHoPxhHm7pceiMJXAfA6GzwHsYboVF7P+HGYaGhnzyySfMmjWL6Ojo+vcWQpBUmERsZix7ruzhzIkz6JE/anbGdnhaeDLac3QDwnUwdZC9rtuAugKMjiZiMzMzystvyNKEEESfz2Ggj43chVoIns7OYpeRgtVZMbz2NyI2MTFBpVJ17KK60OG4U+RrTu7u7s2z6C1QXl5OU908moIkSYQ5hvF65OtET47m5YiXMVAY8O+j/2bYj8N4du+zHMw8WF+tV1hYiJWto5x3fPokjFwOmcfhs7tkd7djX8i79K2AhYma18YF8duTkbhaGvFpQiXT1x/n7NW2V/rdChUVFaSnpzepTQ7xCGF15GpMhAmP/PUIR68d5fGQx3Ezd2PZoWVUaatg+Muy81rMyhvKiexzDeaps8A8eu0oEhKXUr0YHuDQ4JidZ6/x5HcnCHLWsH5aMNXHviU48W0kx2CY9kO9v4UkSfj28OXlfS/zxO4nsFGZsKbWk03aIyh/exIq8olW3sUqwyfhwa/lfL5CiY2NTb0T3rx584iPj6e0ppSdqTtZemApI34cwaTfJ/HB8Q+ooYYRmhF8cfcXHHzoINGTo1l3zzpeiniJaQHTGOAyACczpzaTMMhSs7Z07mgtFApFfaABcDGnjIzCSob5X/89Xz2O67WzPGQTyi/Jv3ChsLEfs0ajQZIk00YvdOGOwZ1ExO3eqCsrK2tXJGJuYM5kv8lsGrOJn+77icl+k4nLiuPRXY8y6udRrD6xmryaPFSq6zcOBiYw8GlYeAqGL4XSa7D1GXinO3w1XpZLVdzaMDzIxYJ3o1xYPNiRlLxy7vsolld/O0tuaevaH7UGp06dIjg4uNm7hED3QFYPWo2FZMHjux7nePZxlvZfSlppGp+c+gQsXOVOHqd/BLWRbJyU8zcirirEUGnI/oz9uJsGoa01Y0TADWXJgeQ8nvz2BEEuFqyeFEDeoe8IOfcmkq0vTN8s55+v40TOCab/NZ1D5QeZWangu9MH6H/tEH+kqrg66ktqHjnAMz+lMGLcQw3WUNfjLakgiWd/fBaPFzwYvGkw/9z7T3Zd2UUv+14sH7ic6EnR/Hjfj8z0momn2rNpT+vbgLm5OWVlZR06Zx1MTEyoqJAbAESfl4th7vK/nsWL3wBqEx4Z/DpmBmZ8dPyjRuOvF6R0rDtVFzoUd0RqQqVSObu7u7cupG0C5eXlmJre3gXfz9qPF/q+wDN9nmFP2h5+vvgza0+tRUJix187mOA7gWFuw2RXM0NzGPRPiFwk9387sxnObobfnpKJ2XsYBE6QN/2MmtYRF+TnM3OQP9OHGvHuX0l8dSiVb4+kMbG3C/MGeeJj336iyM/PR6FQtNgJAiCgWwCrB61mQewCnox+kveGvsdY77GsP7OeUR6j8Ov/DzjyKRxdBza+jTbsCqoKqNZVc6n4Et1VM7E2NaB3N7m4I/5KIfO/OoanrSmrHvAn8+CP9ElciWTpBjN+qTedr9XVsvrEKr48+yVOesH6a9l0VznBPW8h9Z6CSfQBhs5ciE63mDlz5hAYGMjSpUsJ6hOEVS8r3v/lfdKUaUjmco7fw8eDkd4jiXSJpKddz0ayRTs7O/Ly8rC1bb9HdVOoi1z1en2jzcDbhampKWVlZZiamhKdmEMPJw1OFsZykc2pHyD4fi5WXqNSW9lkNN+tWzcVMhEnd+jCutBhuCOI2Nra2tfZ2bndn96KiooWq5/aAkOlIaM8RzHKcxTxyfFsS93G/qL9LN67GEtDS8Z4jWGC7wS6W3WXFRSOwfJj+FLIOnmdlH+Bi4+D0kDOJwdOlAskrht7CyEoKyvDzMwMSZJ4bVwQswZ4sC42hZ/jM9h0NJ1h/vbMH+RFhFfLhSRNISkpiaCg1vWI6+7WnVWDV7Fg3wIW7lnIkoglxGbGsuzQMjaO3ogyaKIsZesW0SgizizLBGQ1wcUUT0b42aFUSCRmlfDwl0ewMzdkzYM9uHbkF8LOvY5kagszf5X7DAIX8pN4cfcTJFVmc39pGYuVTpiOX8lVTW/y8vPpaWRBVFQUUVFRCCG4UHiBdafXkTYgjd9zfkcbo8Xczpx7nO8h0iWSSJfIlot4kFMIdVapHQ0zMzPKysrQaDrWp9rExITKykrKq7UcTytk3iAvWfu+9RlQKMkIf5hFMYtwNXNleeTyRuM9PDyMAefGM3fhTsEdQcSGhoYef/dxaAsqKipanSNuC0xqTZgfOJ8lDkuIy4pj88XNbEraxNeJX+Nj6UMv+16E2IUQYheCu8YdhXNvuYR65GuQcQzObpEfSdtBZSTnNQMnUuo0AHNz8wYE621nxhsTgvnnyO5sjLvCxkNXeOizOIJdLJg3yJOoYCfUrfDjLS4uRqlUtokMvF28+WjwRyzcv5AVcSsY6DyQ/Zn72ZS0iWkDnpbTE2lxUFMmezZcv6BcLZM9Fnw1PYkvM2ZkgAMbNv/BK/uKQK9jpD6NvOPphJ9bgWRoDjN/o9rQhpkPTqLS7gTpfYzQCD0f1Zgw9K7lsimTQoGTEFy4eJHCikLic+PZn7mf2MxYcirk23J/a39mB80m0iWSELuQlot1/gZDQ0N0Oh06na7Fzd32QKPRUFJS0ilEnJ+fT/yVQrR6QX9vGzkSvhRN2d2v89TR19EJHauGr0Jj0Pi9u3XrZmxsbNz+Trpd6HTcEUQshHC9nYj25vLSjkR5eTmurq4oFUoGugxkoMtACqsK2Xp5K7GZsexI2cFPF34C5DLVnnY96WnXkxC7EIIdgjF3ewPuXiEbe5/dAud+gcTfMVMZ4+cSCSYzZXJW35BE2ZgZsnBEdx4b4s3m45l8HnuZBZtO8tafSTw80IMHw90wN2q+QCAtLa1eT90WeLp48uHgD1m0fxGxmbEAfHD8A4aN+xUn72Fw6boSITcJXMPQCR1Z5bLHgpk2FAOlAk9bEx7/NA8LGzvWPRTIcw8OYqWxhEKthlm/gWU3fvpwHoqhZ0gxMWZwpR7XBGuGrt4H12/tLxTICoe/Cv/i/E/n0Qkd5mpzIpwjGOQyiIEuA7E3uXWFY0uoI8zbdbr7O8zNzSku7viNV2NjYyorKzmUm49KIRFmp4fP/oXONYznK86RUpzCJyM/wV3j3uR4JycnLC0tu+RrdzDuCCLWarX2Dg4Otz6wGQghOjwvB1BZWdmoJNbKyIoZPWYwo8cM9EJPSnEKCbkJnMo9RUJuAgcyDyAQSEh4W3rXE3PP/o/gdc/rKNLiKNz/OVZZ++CHv8DADPyi5Jyyz/B6na6RWsnUft2YEu5G9PkcPtt/mRXbEvlg10Wm9uvG7IEecp7wJuj1evLy8ggMDKQ9cHd25z+D/8Oz+5/lXOU5KrWVrDi8glX9n0KqI+Kcc+AaRqH2hr3muWR3QtwsmLPuIAojUz6Z2hPtxT1sHqdFW63FYO52RG4Sv2yZykeaMkDJim5jiRrwMs5eboQ9v5sDVw+wP3N/fdTra+nLcIvhPNTvIULsQ26v793f0FlEbGRkRHZ2dofOWTdvdXU1hy5VEeJmiWnMK1BVzH98+7Ev9Xde6vcS/Zz6NTveyckJtVrdNEt34Y7AHUHESqXSsF6Z0EZ0ZkGKTqejpXUpJAXelt54W3oz0XciIBu+nM47XU/Mu67sYvPFzQCYqc0Itg3G2sqJkQM/Jay2GosLO+Sy6tM/yG11/O+VSdlrKKgMUCgkRvRwYEQPBxLSi/hs/2U+j01hXWwKY3o6MSnMjX6e1qiUCgoLC7G2tr6ti5KbkxvvDnqX5/c/z6nKU+zL2McOzzGMcgiG7NP1G3b52htSrdxiI3KLC1FKgqDCAyjP59MncSU1SsHOUj/8f53PG7ps4o2NsMnRs/zej8lVF/BYzBM4LHdg0d5FmKnN6O/cn0iXSAY6D8TB1IHY2FiCrYI7lIRBJuJr19puV3orGBkZNesffDtQq9UUV1RzOrOSlSG5kPAdW0LvZ33q70zxm8KD/g+2ON7JyQmdTte8l2cX/uf4nxOxJElKT0/Pdq9Dq9U2NDLvILSX4M0NzBngPIABzgPq50ktSa0n5oTcBOIK49gWuw0AD40HIQOm0hNDQnIu43N+G8qEb0FtIuebXcNk/2TXcELcHFk1NZT0ggq+PJDK90fT+OXkVWxMDbg70JFgixoi/Rxv+9xdnVx5e/DbLIldwrHyYyze/xwREYux/PUpuchj1ErOVsreE26K0dRt4d3nWI5pahxhp79Dqi2nVGlGolsqS9UaTIwsuNt1MDvO7eSZ+Gep1lfjofFAG6dl1T9XMcR3SCPCrfPjvbkgpSNgbm5OcnLHCwgMDQ07hYglSeJioQ6lvob70t/hjJ0XrxWfIMIpguf7Pn/L8dbW1mi12o4N/7vQofifEzFga2dn1+6qutra2k4h4pqaGgwMGjfgbCskSar3JBjnMw4hBDv27MAqwKqenPdlxvLr9eIIk25OBJv0oadWEFKcR/DhtVgf+ECezMINXMNwcwljaUg4z40YRMylEradvsavJzP5rkaH1YF8RgUVcG+wExFe1q1quNkUnB2dWTloJU/EPMGFqgssztlHXQ+I0tJSMmtkxURiUggAM/u6MCDlY0b5nUFfC7+ZmfKutSWF199fq1CwM+0vFD4KIswjeGTgIwRYBuA034nhnwxvUhlia2tLRkZGhxOxoaEh1dUdp9muQ2ekx+qQXqpnoOIMBmVpvObeH2tRyztD3mnVRqUkSag740vShQ7DLf+KkiR9AYwBcoQQQdef6wWsBYwALfAPIcQRSf42fQBEARXA7Dr7PUmSngFmAP8WQnx/01uYmJmZtdspRavVtpg+aC86ioj/jurqaiyMLejn1K8+ryeEIL00vT5iPpV7ii9KL6BT68DNgW7G9vRUWRJSVUXPrHi6n92CCjBSqBnlGMwo13BqJvRhw+laTql6yKR8JA1rUwPuCXQgKtiJ/l42bSZlRwdH1gxdw6rDqxjkNYhLqkhqsy9QlpTEeJPxpBrk85XeEm8HUx4u/AjP0p9INFDzho01J41uGO8oJAWhDqGM9x5P0vYkEv9MpOf4nmzatKlFoxyNRtNkm6PbRUca8zQFIUSHv0dxNYxRH+NnK1sSKzJ5a/BbWBi27HV9M5RKZasXJEnSKOTvsRL4XAjxpiRJgcDnwAXgYSFEu4OnLjRGaxhsPbAK+Oqm594Clgkh/pAkKer6/4cCowHf649+wMdAP0mSzIBwoC/wM3AzEatu52LdWUTcGfImaFrhIUkS3TTd6Kbpxn3e9wFyL7az+Wfro+aDuQlsrS0ACzC27k4PEye66yWcywpwPP89TglfMk6rY66hFcIvjEsG/uwsdmPDyVK+O5KOlYma4QEO9PW0JtzDGg8bk1aRhYODA4/1eYwTJ06gCByC37BZSJJEWUwZ0wZP4y63U3gcfAHzzMOssLHiR3Nz9Nen1dRqmNNvDuc3n2eQ5SBGeY5i6NyhzJgxAx8fH6ytrdm0aVOz761Wq+tN2zsaCoWiU/7GCoUCvV7f4fOWVOvoozzBdEsrwh1DGeUxqk3jpVZeGSRJUgKrgZFABnBUkqTfgEXAWGAKcDfwZ5sW0IUWcUsGE0LskyTJ4+9PA3WCRQugrmnXOOArISdY4yRJspQkyQkou2lcozXcDhHrdLpOuSXsjC8TtP7CYaI2IdwxnHBHuXOHEILMssx6Yj6Ve4rfSlIol8rBRkPdn0OFhGNNIk6lx3HSapllrcNKbUOl3pXki05sPenMp3onKk1cCPZwItzTmnAPK3o4aZqNmLOysvDx8SEtLQ1nZ+d6b4eysjJqywrJt7LhIXMnipRKzA3MifKMYqz3WIJtg2Wyv6mPsJGRET/++GOrf18qlapTLrZ183b031ipVHbKZ8elMokNVhJlCP7V91/tibglSZIkcevNj75AshDi8vVBm5C/10rk768e6Nxbiv8P0d5P90JghyRJ7yD7VdRZiLkAN/cXzwBchBDHJEk6DRwD3v77GtRqdbv/sJ1xGwidFxG390sqSRKu5q64mrsS5RVV/3xpTSlXy66SdDWJS7mXQANZ5VlcK83gcEk6uTXF6NECqaBJBcBKp8NFq0MqlTgbb0jSYXOEzgaNSTccbXrg6toTNw8/fBytQFdLVVUVYWFhWFtbExcXR0REBHq9nvj4ePr06UNZmB/+O15hYuhEhrkPa9w77jZQFxV3NBHXEWZHQ6lUotPpOnzfwpkYNpibMd1vEr5Wvu1aF/J3tekusDfQ1He4H3KqYhtwETkt2YUORHs/3Y8DzwghfpYkaTKwDhjR0gAhxEpgZVNrUKlUt0XEnRERd1ak3dEEb25gjp+1H5pqDX5qv0YdKGr1teRW5JJVdpWs/AtkFSSRVXyFrIprXKsu5KqukgqpGCgGLkNNDFyGVw/nY15iylzDd3k9ygugvlVUTEwMVVVV3HXXXWg0GjRomGwxmTCrsA4lYZCj7qqqqg5trAryhmN1dXWHz1tSUkJ1dXWHFhhdy73EeudLgMQ/Qhe2a45Lly7ZIu/plN/q2KYghDiBTMhd6AS0l4hnAQuu//tH5CQ+QCZwcyml6/XnWoJUUVFhFhMT066F1NbWotPpOlxI39nztrbzb0fMK4SgTF9GoVZLVbUxqmpTNDVm6PQ1SEJPKlXU/u1SmKdS4iblkldaweW0dCqLZatPnU5XL9E6duxY/cWqoqKC+Pj4Do9cy8vLO23eY8eOdfi8lZWVHD16tEPnzStLrf933IE4VFK7525NBNCe73AXbhPt/YteBYYAMcAw5NsVgN+AJ6/nlfoBxUKIWzGO1tDQsHTo0KHtCiFycnLIy8trdU+5tsybm5vb7iq15pCdnU1+fn6HrrdGV8PZtLNcuHaBKrsqOTVRlsXV4hSulaSTVV1INQ1vw431epy0Ouy0AjetAepaU1TCBo2xG3ZW3fEM7cNFL3/2mJuQlHiWiIgISkpKiI+PZ9iwYRw+fBilUklERARVoop3dr7D1F5TCbBtXyfu5hAXF0dISEiHR66HDx8mODi4wz1KOmu9yf/+lm8cs0i3SeHhnvPbPN7Hxyc3OTm5ohWHHgV8JUnyRCbgKcDUNr9hF9qE1sjXvkNWRNhKkpQBvALMBz6QJEkFVAGPXD98O7J0LRlZvvZwK9agralpf6dvSZI6pbquLtfXGfO2Nzep1Wu5WHixfrMutSSVrPIs8ipvMqa/7gtupxM41dbQXatlsB5MlXZU1NiTU2pNXrUT13SuSLae2Ht1I9zDijB3a1ytjJvMt+v1ejIyMrh48SJhYWGYm5ujUqkICAggLi4Ow8Jf+b3oL37Z9gsB1gGM8xlHlGcUVka3X0PQWaqYztqM7ay9hVLdXQwt/5yPE9YS5T0WB9O2WQLodDqJW+eHEUJoJUl6EtiBHEF/IYRo3Dm2Cx2K1qgmHmrmpT5NHCuAJ9q4Bm1tbW27mbROhtTR6Ewi1mq1rTo2rzKvgUribP7Z+s7BNgaWdDewZIjeAMdaQxyLruGsrcFJq8NB040q214cU3nzc44Tn+TZopNUhLha0i/MmrvdrenjboWVaet00l5eXhw9epTQ0NAGBvz29vbk5+fjeGQvP9VksdLGiiMFiSQeSeSdY+8wxHUI47zHEeka2e4y5c4i4s5QTEDnEfFl42BeK6hgiqkZ7x57l7eGvNWm8Xq9nlYoJgAQQmxHDqq68F/CnVBZV3s7WtE6GVJHo04P2tFozo+gVl/LhYILnMw9WU++dX6/KkmJv6kLE43c6FleQkj2BZzL02QNkaEGXPogQsez56oB22yGsvl8JRdOlSFJEO5uzUv9HRkd7ISDpu3Zn5KSEn498StB/kHknIul5EQeks9wCisK+eyPTXx8xIKBHh/yet4CPr92kR2mJrxta0sOWnan7WZ32m6sjayJ8oxivM94/Kxb385eq9WiUCg6TRXTWZF2Z2zymhgacLk4hLnlqXyc+gcPdH+Avk59Wz2+tSTchf8N7gQirq6srGz3h6SziNjAwIDbSZk0h7ry2pyKnEbRbrVOLru1N7QmxMCaKYYehBRkEpB7GSORApIC7ALAb1y9/8QFvRPbTmez/WQWF3PKkKRcwj2sWTY2kFFBju0i3zqUlJSwbPcydpbsJEwK48s42bzoamgiP5f+TEJVAqXVS/k9UY//XV8Qde1jRqV8y+CKdD611LDBwgKtJHfy+CbxG75O/Bp/a3/GeY8jyisKayPrFt+/zjy/o9HZnNQZFw4LQ9ha04e3c+P4zaY3bxx+gx/v+xG1snV3Gl2VcHc27gQizs3NzW13CKFWqzuFiDvSj6BGV0NiQWI98R5JP0JhquwtoVaoCbAJYLL7KHqWF9PrynEcUk7K0a6pnUy4wdPkn869wdCcqlodPx/PYMM3qVzIviRHvh7WPBpuxdhebgR6374HeHFxMSv3rGRnyU4AXnYZCchE7OzsjJFSJvjuvme5kBTOOzHpuE9cRK2BJd2T1rCwsJhxFTW8aWnGQRNj7Aws6O3cj4zSDP599N+8e+xdBrkOYli3YUS6RGJr3Lh1UV5e3i3bPbUHneVP0pkE72SqYIO+FyoDS14s1/FE1SWWxy1n2YBltyR+IQS1tbUd/yXpQofhf07EQohaV1fXdidj1Wp1p0SutxPVXCu/1sA34lz+OWr1cvrFydQJL2MvhvoOpbe5CwGZZzE49ytc3SoPdgmDu18H/yiw8pTbMV1Hflk1X+27wMa4KxSU1xDsYsFr4wIZFeiIvUb2ws3NzaWh+qjtKC4uZunupUSXyh7Ei/oswiv+eilyn9kA9DbtzeHywxSpdwDhCAEvbrvMuoce56xaQ4/E9/E0tmOt531EJ/3EW6Z57EjdwSTnobwY9Q1/XfmLbZe3sSd9DwAB1gFEukQyyHUQwbbBqBQqcnNzCQkJua1zaQqdFWl3lj+JEAJ/ayVlmBDjsZARSa/wSNj9fJq8BW9Lb2YFzmpxfElJCQqFoqTDF9aFDsP/nIgBdDpdTXs3OTrTwKU1fgTVumrO5Z9rYHNZZ25uqDQk0CaQaQHTZHN4u57Ya3Vk7lqD/cENqK8dlydx6gUjlsk+xFaN/bsv5ZbV97Or1uoZ7m/P/MFe9PNs2M/OxsaGxMTE26o2LCou4l+7/kVsmdylo4dND2ZahUDK9UICB7kXno1KjlQrdWWYm9Tib2/PpdxyFm5JZu2kGSSozAk5txLp4k6Gz9zJgDM/8/HpT1mfuYe4qwd4I+x5Fk3azfmC88RmxhKbGcsXZ77gs9OfoTHQEOEYgX2FPb6SLyZ0rMSsM9oZQdONBDoCWq0Wa1MD/B2VrC+LYITXUJ44tZOU8Pt4L/49PC08Gew6uNnxWVlZqFSqq80e0IX/Oe4IIlYqlXl5eXndbrdLR0eTct3G2s0donV6HYeyDhGbGUtCTgLnC8+j1ct3fS5mLvRx6FPfx87Pyk/O4ZXlwLlfIfo9uHIQFwTVVr4w7GWZfG28mzyfIykFfLY/hV2J2RioFNwf6sLcSC987JuO5lQqFRqNhoKCgnbd0hcWF/LcX88RVx4HgFJS8tqA11BG37RDby/rn+uIGCCkeybHzxmxcW5fZn1xlIW/JLPm/gmclJT0OvMa0ndTMZ69lUV9H2XI3tdYkr6NWUeXM+f4Wv4x7B0Ces5nfs/5FFcXE5cVx/6M/exL30dhTSFf//A1PWx6yNGyixwtKxW3p0ooLi7ucGtN6LyWXVVVVRgaGhLhZcymo2lUP/Uuhp9GsiKviAwrP57b9xxfj/4aH6umuyFlZWWh1WqvdPjCutBhuCOIWKFQZGZlZYW2l4jrCLOjo5Gb25hnlGbwS/Iv/JL8C9kV2RirjAm0CWRmj5n10W6DPGd5Ppz4Gs5uhtRYEHqw84eh/6LYbRiXipWEhoY2ek+tTs8fZ67x2f7LnMooxspEzdPDfZnZ3x1bs1uXD3fr1o1BcCx2AAAgAElEQVS0tLQ2E3FBUQGL/lpEfEU8fRz6EJ8dz6zAWfhJhnK/vTrYywUbakmNrbEteZV5aI1PUlHjQVm1jnWzwpj5xREW/XaZD8eP45S+hp5nXkfaOAFm/Uafu9/i59JneGvnP/i8LJnYbVN5wywI32HLsHAM4h6Pe7jH4x727tuLpa8lR3KPsD9zP5+f/pxPT32KxkDDQOeBRLpGMsB5QJO55VuhsyLius9KR6Mu0o7wsmH9wVQSyq3pO/QFTHa9wofjPuKhi1/yZPSTfHfvd01qt7OysigtLb3U4QvrQofhjiDi2tra1KtXr9KrV692ja9rrtjRRGxkasS2S9s4mHCQw1mHkZAY4DyAxeGLucvtLgyUf8sHVhZC4laZfC/vBaEDGx8Y9Kwc+TrI0aS5Xk/x3r0NhpZVa/n+aDpfxKaQWVSJp60pK8YHcX+oK8YGrY8AbWxsOHv2bJt+H/lF+SzYuYCEygQeD3mcbZe34WbuxuMhj8POpbJawyMS8i6AyQ2lg4uZC3mVeVwoicfIcDS7E7N5bVwQa2f04ZGvjvH8tlTeGzuZM/pags6+ifTNJJi+GVNzJ5bdv4Whl7bx6sFXeLAmiQXfjmKGyzAUd/2LPIUdpiamhDiFEOIUUh8tH8r6f+ydd3QUZfu/r93NpveyKSSk0hJq6C0giFKkiIqo2Bsg+GIBu2JHQQQRRbDwAoIFERCkKC2EkgQC6YSEFEJ627RNts7vjyGBkLZp3zf6y3XOns3ZnZl9Znbzmfu5n7ucIexaGKeyT3Eg/QAguk7GdhvLmG5jjLKWtVotgiB0yGJdWVkZfn5+7X7cWiF2c0QigbOpRQwbvwjiduJ25EPWzv2ex489zwvHX2DTpE31IikyMzPV5eXlXRZxJ6ZTCHFxcXFydna2QCvL61laWqJSqXB0bDocyliSipP4Lfk39l3ZR7m2HA8rDxYOXMgs/1m4W9/Sbbq6FC79KYrvlWNg0IKDD4x+HoJmg1u/OgtuIPqeLSwsUKlUmJqZs+1sBqv/ukxZtY5hPo68Mz2Q2/u4IpW2/HJIJBJ69uzJ5cuXjVroKigpYPHhxcRXx7Ns6DJKqku4Wn6VTXdswlyjggtbod99YtNQRd30ZQ9rD6ILotEatPTyy+RIoj3vzhC4rZeCNfcPYvGOKN48ZMJHk+eRYNASmLASyY658NCvILfgNv9p9PcYwXun3mKV5CTHSyN4f+MYzJ1GEjjueRCE2mtnZ2bHZJ/JTPaZjEEw1PEtb4rdxDcx32BnZsco91GM9RzLKI9ROFnUnxW01m1jDOXl5XUSXtoLlUqFg4MD9pamBHnYEnq5gOcn9oAZ62DTBPonHOC90e/x6slX+STyE94c8Wad/dPT01XcKFXbRSekUwixRqPJunr1qgpo1bzOysqqzZ0cyjRlHEg9wK6UXSQUJSCXypngNYEe1T14+s6nkUpuirAzGCBpP1zcASl/gV4jtjEaMV8UX49B9cT3VpydnTkak8768CISc8oYE+DMS3f0ZFD3tqcFu7m5kZKS0qww5Bfns/CvhSRVJ/HWiLcY4DKAufvmMsN/BiPcR8CJT0GrgpHPwbcTYehTdfZ3MnfCwsQCezN7pJIYspQBXMotp4+7LdP6u1Op7s+y32L40FTGW7c/wSWDht6JnyP5eR7M3Q4mZjhZOLFm4nr2XNnDivCPucfLnFeK4rn7l/vA0Q8GPQwDHwSbG734pBIpgU6BBDoF8kz/Z0RrOfsMJ7NOcipLtJYlSG74lj3H0tepLzKprMNC4gRBQBCEDsmqq6ysrPVp39ZLwfpjKZRUanDwGAR9ZsCFH7l93DIczR1JLkmut39GRoYWaN8qU120K51CiIGcjIyMalopxNbW1mRnt/yGLwgC5/LOsSt5F39l/IVar6anQ09eHfYq03ynYW9uz/Hjx8Vy2BJEC+3yQTj6odjR2MZDFKeg2WKTTyMXCwsr1HwZoWR3TB7uduZ89VAwU/q6tdtio0QioV+/fkRHRzN69OgGj5tTlMPCvxaSqk7l/dHvM91vOg8feBhbM1uWDlkKVUo4+zX0uAPkFqCrrmcRO5o7UqWrYob/DLFTtVR0T/RxF/2vc4Z6Ua7W8f6+BExkUl4d/yyXDRp6JX0JO5+A+zaDTI5EImFWwCwGOQ1iyaElvOOUwgm/YN4uqcDpyLtw9APoORmCH4aASSCr+7O1M7Njsu9kJvuK1nJicSJh1+pay/Zm9ox0H4lTuRNP+DzRLtf5ZjrKPwyiENcce0JvBeuOphCaXMDMgd1g8KOQsJsfQ9+huLqYlSG3lvuGrKws6BLiTk1nEuJWxxJbW1tTWWl8mdV8VT57r+xlV/IuMsszsZZbM9N/JrN7zCbQKbCOcNnZ2aEsKcFRGSMKQtY5Mb539iboew+0YAVfpzfwY/hVVh1OolqrZ5qfnA8fHIW9dfuHPNnb2+Pg4EBqair+/nWjMrKLsnn28LNkajNZEbKCKb5T+DHxR2ILY1kxdgX25vZw+E3R5z3hTdEtAbUREzXULAwNdRvKz0k/4+edwd+J7iyacKNw+ZNjfNHoDHxy8BLFlWrev/M5kg0aelzaCL/Ph9kba69hSUYJn4/8nBMVJ1gbtZbZljYsv+9rbstOgovbxVmItRsMeggGzRMt5luQSqQEOQUR5BTEswOerWMtn7x2khJ1Cdt2bsPFwqW2qauvnS++tuKzq5Vr3dmPkRQXF+Pg0P6Nkmss7Zq06QGe9jhZmXIkMV8UYt/xKB268232EUI8QxpMe1YqlQBdccSdmM4ixFnp6emtNgelUimCIDSZ5681aAm9Fsrvyb9zMuskBsHAENchLBiwgNu9b8fCpGEx9NBdxfznFyE/Cmw9YfoX4lTZyNTSGs5nFPPW7ngSrrshls8IQld8jQplEfbW7R9KBdC7d29Onz6Nvb197XQ8syCTZ/9+lhxtDp+N+4yJ3hPJqchhbdRaRncbzVTfqVCSDuHfiOfpPgCSDgIScKlbJ6JGiD2tPXGzcsPUPI7oi73JL69GYXMjjGvBeH8UNma88lsMC3/T8NmM/5CqV+MX918wMYcZ68jIzESn0+Hd3ZtHJY8yymMUr4e9zvPnPubugLtZtigC6/RTELUFwj6Hk5+Bz1gIfhT6TAd5w2FjN1vL8QnxFEgKSNOnkVqaSlppGn+m/Um55oZby8LEAh9bH3zsfOoItLetN+YmjYemFRYW1rvhtQeVlZV1SnVKpRLG91Lwd2IeOr0BE5mUb7r3obI0gRcD7qu3v0ajQaPRVHfVmujcdAohFgRB6+7uXlZZWenS2umdjY0NFRUV9cKS0krT+D35d/Ze2UtRdREuFi48HvQ4d/e4G2/b+skTtWRFwbEPcU35G42pA0xZKU4DTVrWgaKwQs2KA5fYef5aPTdEpZUX0dHRHRLTCmKltyFDhnD27FmGDx9OQWUBz/z1DIX6QtZOWEuIZwiCIPBB+AcAvDXiLXE28PdykJqI1jCIFrGDD5jW/W5qakWUqEu4w/sOtifuQJDcxfGkAuYMqZvdd89gT1xszFiw7TxP/5zE6lkvITWo8bm4jWqDhAyn+xh1kxulh0MPtk/dztfRX/Nd3HdE5Ebw4ZgPGfzQL1CWDRd/hKitsOspMLeH/veLrgu3fjSEwWAgPy+fkJAQxsvG174uCALF1cWklaaRVpYmPpemEVMQw8G0gwjX2yxKkOBh7SEKtK1vHWva0cyRsrIy7OyM76psLKWlpfWOO6G3gt+irhF1VYm7UyU/lSdzd0Ul/snHwXt8nW3j4uIwMTGJbfeBddGudAohBpDJZOcvXrzoP3r06Fbtb2dnh1KpxNbWFpVWxeGMw/ye/DtR+VHIJDJCPEOY3WM2Y7qNwUTaxGnnxcOxj+DSPrBwhEnvcba6N2OGTmpRVS29QeDH8AxWHUpCpdEzf5w/iycEYGV247OtrKzEjsgdlHILYmjfwIEDORh2kPUF6ykVSvly4peM9BgJwKH0Q4ReC2XpkKV0s+4GmRFi3PC4V8DWQzxIfmI9twSAg5loEZdUl3CHzx1sSdiCrVMSF672qCfEACE9Xfj52ZE8vjmSZ36+xMrpS5HoqvGO2crIodaYyOpmh8llcp4Pfp4QzxBeD3udxw8+zmNBj7Fo0CJMQ5bCmJcgPVS0ks//ABHfiAulwY9A33vB/MZNOS8vD2dn53qLaRKJBCcLJ5wsnBjiNqTOe9W6ajLKMuoIdHppOlF5UbXlSAFs5Da4yFw4cupIHYH2tPFsdfnPGpRKJdYO1uRU5FCiLkFZraTarAgzx7OsOX8OLJKQy+Q85xAMF36E296oM1s7d+6cvri4+EibBtFFh9NphDgvL+/viIiIu0ePHt2qX669vT3nUs/x/bXvOZh+kEptJT62Prww+AVm+M9oPvC/MAWOfwxxv4GZjfiDHj4fzG2xuXABpVJpdHjc+YwS3todR0JOGaMDnHh3RhABioajF7y9vUlPT6dv374tPWWjKVAX8EX+F1QYKlg7bm2tCJeqS/k44uPaNGwEAQ69DtauMOp5cWedGopSxOn/LThaiNejuLqYu/zuws3KDZUhnujMsY2OpW83O3YtGMWjP0SweNdlnuj9APM81HhGfg2WtnDb6/X2GagYyM7pO1l1bhU/xP9AWHYYH4/5WCyp6TdefKiKIeYXiPov7HsBDr0BgbNEUe4+goyMjBZ3WzE3MaeXY696pTsNgoG8yrxaKzrmWgxXK69yOvs0e67sqd3ORGKCl61XPQva2cKZMk0ZSrUSZbWyVmBvfi5Vl1KiLqFIVYRWqF8m1tQVYisk2OvseHnIy7iogeS/xRupzw1jJjQ0VKlSqcJbdOJd/J/TaYRYp9OdCw0NVb7wwgsurdk/XZPO20lvgxQmeU9ido/ZBCuCm49EKMkQw7Sit4v+yjEvwKjFdRIX3N3dycnJaVaIBUFgw4lUPj10CVcbc9Y/GMzUfk1HQ7i5uXH58uUOKxiTkJ3AgqML0Eg1rBm5Bk2qhiLrIpycnFh9fjWl6lK+mfSNmAgRtwuuRYrxqWbXLfTCy2Jiimt9i9hGboOJ1ISS6hIkEgmTvCfxY8IO8gryqdbqMZc3vJDp5WjJuhk+/Oe3RL6J12M57lXuE3S4n/hE/A7GvlhvH0u5JW+PfJvxXuN55/Q7zN0/l0UDF/FY0GPi2C0dxfDB4c+KbqWo/4o31ejt6B38cXcZj03QMqDtcb5SiRR3a3fcrd0Z1W0U/qX+9B3ZF2tra8o15aSXptexotNK0wi9FopOaLoAmo2pDQ5mDtib26OwVNDDoQcV+RX069Gv9vWa541Hc9l7Qcnx5VOQSSXwy6NgalPve4qMjNQDF9t80l10KJ1GiIH4ixdb93s5nXWaJceXYCO14YdpP9DdvnvzO5XlwMlVcP6/YubY8AWiCFvXvw+4uLiQmJhIYGBgo6Kq0uhYujOG/TE5TOvvzif39MfarPnLK5VK8fHxITU1ld69ezc/7hYQmxXLgmMLQAbf3fEdgU6BVHlUce7cOYosi9iVvIvH+z5Ob8feouX793KxqM/Ah24cJD9RfG7ANSGRSHAwc6BELZb0vNPnTrYmbAWrOBJyJhDcQEy0Xq8nMTERlUrF78/fxsu/xbH6RBYFwct4Tq/G7ci7YN8d+t3b4DmFeIawa8Yu3j/7Pmui1nDi2gk+HPMhXjZeNYMCz8Hi486PIGE3qtCv8L78HXz2nZhm7jNGXOjzGQtWbYsp1mq1qNXqWteSjakN/Vz60c+lrq9aa9CSVZ5FWmkaRdVF2JvZY29mj4O5A/Zm9tiZ2dVzmSmVSlJTUwnuVz8Vfpi3KT+Fl5CSX0EvWbZYy2TMC2Bx45prtVrKysqqBUEwplddF/9DOo0QC4Kg8fDwKFOpVC4taej4V8ZfLAtdhr+dP0s8l2CuaaboSkUBnFoDkd+CQSdOXce+DHbdGt1FJpNhY2NDaWkp9vb29d7PLFbx9JZzJOWV88rk3swf59eimODu3btz4sQJ/P392y319uK1iyw8thATuQnf3fkdPRzEkDILCwtGjBzBrF2zcDJx4mG/h8Udwr8BZQY8/HvdkLyi6yUKHBuOCHAwd6C4uhiA/s796W7jS5rDGWIyH6knxIWFhcTFxdG9e3eCgoKQSCR89dBg3v0jni1nMsjxX8qntoU47F2MRBHYoBVe85mfjfuMfan7+Dj8Y+7Zew/Lhi7jnh731L3uZtaUB8wkRuXL6B5OcPkApJ0UE3EirzceVwSB73VR9h5VZyZkDLm5ubi5uTW7nVwqx8dOjMYwlqKiokZnYQO8xN9hdKaSXpmrxVjvkXW7lMXHxyOXy+OM/sAu/me0f0+XNiCTyS5ER0cbvf3vyb/z8omX6evUl+8nf0+AR8D1erwNoNfBsY9h7QA4+5WYhLH4PNz1eZMiXIOHh0eDrerDkguZ/mUY2coqfnhsKAvG+7c4MUMqleLn58fly5dbtF9jRF6NZP6x+ZiZmrF5yuZaEa7h6LWjXK26ysL+C7kUd4m4iBMIoSvFZAn/CXUPpioUrSyTht0mDuYOlFSLFrFEIuGRwIeQWWQRejWydpuysjIiIiJISUlh2LBh+PnduFHJpBLenRHEm9P6cDytgodVL1AlmGH46SExfbwRJBIJ0/2ns2vmLvo79+fdM++y+Ojiuo1UgYSEBHGmoegtWowP74JXM+CJw2JUiJUznN8MPz8En/rBhjFw8HVIOtDk59eQk5ODh4dHs9u1hsLCQlxcGvbU+TpZYWNuwtUr8RD7Kwx5QjyXmzh37pyhuLj4WIcMrot2pVMJcV5e3t+RkZFGNbDblrCNt0+/zQj3EXwz6RtsTW1xcnKiqKio/sYaFfzyMJxYAT0mwcJwuPtrMSTLSBQKBbm5ubVdGARB4NuTqTzyfTgKGzP2LhrD+F4Ko493K927d6eoqIiKiopWHwPgdPppnjv+HNZm1myZsgU/u7pJD3qDnq8ufoWfnR/3BN3DmDFj8L36C6grSPR6kKKiorqdJlRFYNn4QqejmWOtEANM95+OTLAktnwfubm5hIeHExcXR0BAACNGjGiwfb1EIuGpsX7sXDCKCjMXHlMtRijJQLfzGTGdvAncrNzYeMdGXhn6CmdzzvLA/gdIKUkBID8/H5lMVj+lWSaH7sMhZCk8uhdevQqPH4Dxr4mhcJHfwo658IkPbBwvJrdcPgzqumn0Go2GqqqqDqkvYTAYUKlUjWbrSaUSBnrZ0zftOzHUcNTietuEhoaWVFZer2naRaem07gmALRabeSJEydKn3/++Ub/8wVBYEP0Br6K/opJ3pNYMXZFbRU0uVyOVCpFrVZjZnY93ldVDNvvFxehpqyE4c+0amwmJiY4OjpSUFCAjb0Tr+2KYffFbCYHubFqzgCj/MFNIZFICAoKIj4+nuHDh7fqGD/F/sSnFz5FYangh8k/1C9QBBxIP0BqaSorx60UF7kKk7FK+Alh8KMo+o4jIyOD2NhYnJ2dcXFxwaWyEKll437Umy1ijUaDslCJt3QUV0yPEpUez+g+Q4yOrx3oZc/+58fyzh5HPohO452UrRQeWoHzlPqRFDcjlUiZFziPIW5DWPj3Qh458Airx69Gnaxm2DAjGmyamIluCe9RwCugrRZ/L+knRVfG2Q1weh1IZGJ4nO9Y8BnDNZ1bh8WAl5SUNJypZzBAzgVIOcrHyr14VMdiGPokUpv67pGIiAgDXQt1/wgknSnhRiKRmHp7e19LT09vcD5mEAysjFzJtsRtzPSfyfJRy+stcFy+fBlzc3O6d+8uRkRsuweUV+GebyFwRpvGV1paStiFBL6K0ZGQU8ZLk3qycHxAq6qkNUZUVBSurq5069a8u6QGjV7DB6c+4Pe03wl2CWb1basbrDymM+iYtWcWZjIzfp3+q5jKu+MBUWyejwJr0aLX6XQUFxeTn5+Pz8GHqDJTkDLkPSwtLTExMcHExIS0tDQ8PT3ZmbWT33J/Y7XXaixMLXB2duZsUTGrkuczxWsuKyc2LaKNsefCNeS7n+ZOznB6xDeMnXK/UfvlVOSw4O8FpJelszhgMU+OerJVn18HjQoyw0VhTg+DrPNg0GGQyKBbMFLfcdB9hHj9LBzEh6m10bVHGiI+Ph5HR0fc3d2hPBeuHIWUv8UKf1XFgIQ8mz78VNKLBa+txdSq7s2uqqoKPz+/jJycHJ+2nXwX/xd0KotYEASNp6dn2pUrV1xuTRfVGXQsP72cPVf2MK/PPJYOXdpgTQB3d3cSExPpLi+BH+8Ti9U8sge8R7Z5fAmFOl49WoIgkfLdo0OY0Lv1HUUao1+/foSFheHk5GRUt4fcylz+c+Q/JJQk8FDPh3h5+MuNJqzsS91HRlkGa25bI167tJOQ9CdMfLtWhEG0/hUKBQqFAg6psereC5tBg1CpVOh0OnQ6HTKZDFdXV3y0PpALA0YMQGEpHsO5Qs2KqCCOZf+BSrsES3nLWx3NHOTJNY+tZG6cQODZl1heYMvL909qdubhbu3OulHr+M+x/7AmeQ2CjcCTfZ9sW0ElU0vwv018AKgrKI07TFXiYdyqLosp18ItpVKkJqIgm9vfEOcmH9e3M7cDgw7t5b9xtSyA3ccg7/p6m5UCet4J/hPB/zZ2Rij5/FASC8zqu0aOHDmCIAgHW3/SXfxf0qmEGKCkpOS/u3fvHvDSSy/V5hILgsCy0GX8lfEXCwcsZP6A+Y3+Y1lbW2N27TTC3yuRmNvDE3vFhZo2IAgC/z2dzvv7E+lma8rbE1w7RIRBdK8EBgYSHR3NsGHDmhSQszlnWXp8KVXaKj4c/iEzejdu8WsNWjZEbyDQKZAJXhPEKe7hN66X71zY8E6CAJWFSKycMTc3r3NjuHz5Mi4uLnRTiZZ7SXXJDSG2NsNOMwGV4Qv2pe5jTq85rbgS4OnqjO7Zneg2jOfulNeZtUbCqgdHMNCrfuRKDTqdjtTEVDbduYlPYj5hbdRacitzeXXYq01nVLYEM2uShe74Tf0IHB2hukwUS1WxWCipoUd5jhgKWFUCmqZKtkoQpCYMNGhBKhct7duXQ8DtYmhhnd+DEqA2Dftmtm/fXpyXl/dj+5xwFx1NpxNilUq1e/v27e+89NJLtSZala6KsKww3KzceCTokSbFSRL7K/1j30Pn4I/8sT030nTbwOd/J/PFkWRu7+PKqnv7cSHiNDqdDhOTjrl8rq6uFBQUkJKSQo8ePeq9LwgC38d9zxdRX6CQK/j69q/p69F0Zt7ulN1kVWTx+vDXxesX/RPkRItV5OSNVH9Tl4uF7pvyEV9Pc64JYathkGIQZ9WebE/czn0972u1RWqi6InJnE0M+OlBFlRt5N6vDbwwqSfzx/mLiQw3IQgCMTExeHt742TvxIqxK3C3cuf7uO/Jq8zjk5BPWmWd30plZSVVVVU3fLjmttf9y0ai14plRhsR7eKCHAyew3EZcveNxJoWYDAYOH78uA440+Kdu/if0KmiJgAEQcjOyckpu166DxCzqlaNW0WBqoCXjr9U25r+lh0hbA3sehp9t2HEDvm0XUR4e/hVvjiSzJwhnmx8eDD2VmZ4eXmRkdGxnWcCAwPJz8+vF45XoangheMvsCZqDQMtB7JtyrZmRVij17AxZiP9XfoztttY0ed55D1x4alvw4kTgBgxAU0KcW3hn5siJwC8na2oLhzNldIrnMlpox70ngZjXuQejvCS/QlWHkriwU1nSS+sW/o0PT0diUSCj48PIC7ivTD4Bd4Y/gahWaE8eehJiqoaiKppIcnJyfTs2bP17g6ZXEwccukpRm/0mgwDH4CRC2HCG8S53Yf9sLmtEmGA8+fPI5PJzglCM6l8XXQaOp0QA2g0mp0HDhyoM98K8Qzh7ZFvcyr7FO+efrduiJVBDwdfhb/fgaDZyB7dTZlGglZrVCRcoxxJzOPN3bGM7+XCh3f3q12U8/Hx4erVq+j1rS6h3CxSqZTBgwcTFxdXG9KWUpLCA/sf4Hjmce62v5t1d67D1aF5F8nOyzvJrczluYHPieJx+gsozxYzz5oqZKS6buU2EzUB1GbX1eBqY051aT8czZz4MbEdZsgT3gS/8cxXf89bPbKIzSpl0ucnePePeEoqNRQUFHDt2jX69+9fb9e5veeyZvwaUpQpzPtzHuml6a0ehkqloqysTPSfdwBlZWVYWFi0KbFn586dFdnZ2T+047C66GA6pRAXFRX9vG3btsJbX5/dYzYLBixgz5U9rL+4XnxRWw07H4fwDTDiObjnOyRyczw8PFrVtaOGi5lKFm2/QJCHHesfDEYuu3GpTExM6NatG1evXm318Y3B3Nyc4OBgzp07x97Le3nwzwcpU5fxnMtzLJ2w1KhOxNW6ar6N/ZZgRTAj3UdC9gUIXSkWtW9uOq26/hU0IcR2ZnZIJdJ6rgmFrRkIJkz0nEnotVAyyto4g5DKxO/WSsFjyrWsGq5m9kAP/ns6nZBPj7Jq30X6DwxutFXRbd1v47s7v0OlU/HwgYe5mN+6qK6UlBQCAgLarZvKrVy9ehUvr/qV6xoir6waU5kU2S1j2bVrV5XBYDjUEePromPolEIMREdFRekasmgXDFjA3QF3803MN/xy6WeEHXPFPPs7PoTJNyw8Ly8vMjMzW/Xh6YWVPLE5EhcbM75/bGid0pU1+Pr6kp6ejk7XsbM/SxtLTkhP8MaZNwiwCeAFpxeYO2au0UkEvyT9QkFVAYsGLUKiVcFvT4nV1aauan5nI1wTUokUezP7eq4JV1txYW+Q/VRMpCbtYxVbOcP9W5Cp8pmYu4mpLsX88vhAfG0Efk7SMO2rcPZGZ9NYSGZ/l/5sm7INW1Nbnjr8FEcyWlYdsrKyEqVSKYaUdQAGg4GCggJcXZuf5Wj1BvbF5HB7oAKTm4yEjIwMVCpVpiAIbWvi2MX/KZ1SiAVBEKRS6bGwsLB679qg1ccAACAASURBVEkkEt4a+Raju43m/fAPmFOdyM9D7qN8yKN1trOwsMDExKTFTUULK9Q8+kMEgiCw+fGhuNg0XAheLpfj4+NDcnL9Zo3tRYGqgKcOPcXOtJ3c5XEX90vuJ2RwiNEirNKq+C7uO4a7D2eo21CxNGTRFbh7g3E1FYwQYhAX7G4VYsX161ZdbckUnynsSdlTpxNGq+k2GKauxCzzJANKDpJ7+QLfPjKYbU8Ox8ZczvM7LjDrq9NEphc3uLuXrRdbp26ll2MvXjj+QotuEPHx8fTp06fDrOHc3FwUCoVRda+PJxVQXKnhnuC6CSV79uzRlpaWbu2QAXbRYXRKIQbIzs7e8tNPPykbek8ulbP2trW84TEJAfigKJyJv07k7VNvE1MQU2sR+fj4kJaWZvRnqjQ6ntwcSV5ZNd89NhQ/l6YXS7y9vcnPz0elav/iVufzzjNn3xwSixNZPmQ5d5jcQf++/YmLi0OtVht1jB2XdlBcXcyigYvg0n6xePqoxeAb0vzOIAqxVC7WZ26Cmwv/1FDTKim/XM1DgQ+h0qn4Pfl34z63OYIfRRN0P/bR3zDEtojExESGdrdh3+IxrLpvAHml1dy34Qzzt54nrbB+L0NHc0e+veNbbvO6jRURK1gZuRKD0HQqdc2iaWO1H9qD9PR0vL2b6BpzE7+dv4aTlSkhPeuOZ9u2bcrKyspdHTG+LjqOTivEwPE///xT29g000xmxtzySn5V6tgxdTtTfadyMP0gD/35EPf8cQ/bE7dj4WBBUVGRUYt2Or2B536MIjarlHUPBDdYwvFWpFIpgYGBxMfHt/jkGkMQBLYlbOOpQ09hJbdi47iNOOY7MmTIEHx9fenTpw9nzpxp1tKv0FTwQ/wPjOk2hoEW7rB3Mbj1v9H+yBhURaI13IwF6GDuUG+xzsJUhq25Cfll1QQ5BTFIMYjtl7ajN7R9gbOwqIgzDrPRK/rhduot+npYcvbsWXRaDfcO9uTYy+N5+Y6enEwuYNLqEyzfG09xpabu+EwsWD1+NQ/2fpAtCVtYemIpan3DNziDwUBCQkKLC8u3hLKyMiQSiVGdWpQqDUcu5TFzYLc6axdKpZLMzMwKQRA6dvGii3an0wqxIAhqvV4fduLEicY2gPQwJD5j6OvSj+WjlnNszjHeHvk2cqmcjyM+5vZfb6fAuqBZX7EgCLy5O45jSQW8P6svkwKNT9ZwcXFBEATy8/NbcHYNo9KqWBa6jE8iPyHEM4SNIRspSS5hyJAhte4IFxcXBg0axPnz5xuvNAf8mPgjpepSnuu/AHYvAE2lmObdkp57lUX1Kno1hKO5Yz3XBIDC1py8MlHc5vWZR1ZFFieuNfJ9GklGRgaJiYkMGz0O2QM/glSK099L6BPgw9mzZ1Gr1ViYylg0oQfHlo5nzlAvtpxJZ9zKY2w4cYUqzY0bgUwq49Vhr/LykJc5nHGYZw4/Q6m6fsW1tLQ0FApFowV42oO0tDT8/Op3pW6IP6Kz0eoF7hlcNw1+69atmurq6m87YnxddCydVogBcnJyPvnss88aDvwsSYeya2KR7+tYya24r+d9/HzXz/x01094WHvwbca3JKclY2iiite6oyn8FJnJotsCeGi4cVPDm+nXrx/x8fFtCpdLK03jwf0PcjjjMEuCl/De4PdIikmqI8I12NnZMWLECJKSkkhJSam3OFWmKeO/Cf9lvNd4+qaehitH4I4P6nVhbhZVkVG+ZEdzR0rVpfWsXVdbM/LLqwGY0H0C7lburV600+v1xMTEkJ+fz8iRI7GwsAAHb/HmkhePIvxD+vTuXSvGILpHPrq7H4eWhDDUx5EVBy4x7MO/eXN3LLHXShEEAYlEwqNBj7IyZCWxhbHM+3Me18qv1X5uRUUFmZmZ9OzZs1XjNga1Wk1JSYlRIXEp+RV8eSyF3m42BLrfiJoRBIF169aVKpXKjR020C46jE4txEBEZGRkWYOlLdOvL+T5NNwfLcgpiDdHvElOZQ6n9KcaDWVLyC7j878vc/egbrx0R+v+2SwsLAgICGi1i+JIxhEe2P8AxdXFfDPpG+7zvo+oqKgGRbgGc3NzRo0ahVqt5uzZs1RXV9e+tyV+C+WachZ5TYG/3oYed8LQp1o+sBrXRDM4mDsgIKBU13XpK2xuWMQmUhPm9p5LRG4EScVJLRpGeXk5p06dwtramiFDhtTNaAy4XewvGPMzioy99OnTp44YA/RwteH7x4ayc/5IJgW68uu5a0z/MoypX4Tx39PplKq0TPadzMZJGymqLmLen/OIL4xHEASio6Pp379/o2Fx7UFqamqdGs2NEZdVypxvzqA3wJq5A+tsf/78eSorK6MFQagX9tlF56dTC7EgCIJKpVr/ww8/1HfeZZwS6+Q2YeUNdRvKNL9p7Mvbx5lLZxoMa/r4QCJ2FnKWzwhq02q4p6cnarWavLw8o/fRGXR8fv5zlhxfgp+dH79M/4VAq0DOnz/fpAjXIJVKCQoKwt/fnzNnzpCVlUVJVQnbErcxyWsivf7+UEy/nbm+dZXAjBRiSxMxbVilq7toqbA1o6BcXXvd7+lxD+Yyc6OtYoPBwJUrV4iKimLAgAGNi9XYl6DnZDj0OgpZeYNiDDDEx5HV9w8k4o3beX9WX2RSeGdvPEM/+pvnd1xAU+HDlslbMZOZ8fihx/nl3C84ODgY3TS2NWi1WnJzc5stp3kuvZgHNp3FQi7j1/kj6e1WN4b8888/L8nOzl7RYQPtokPp1EIMUF5e/v1XX31VVk9Ec2PFimGGpuN4Xx7yMmYyM34v+72eVXzicgEnkwtZPKEHdhZta1EkkUgYMGAACQkJRkU1FFUVMf+v+Xwf9z1zes5h8+TNWOotjRbhm1EoFIwePZqCggI++usjVFoVC1V6sRDNzK8a7MPXLAa9WPugiaLwNWgM4kKYmayu/1lhY45Gb0CpEl02dmZ2TPefzv7U/fWiLG6lpKSEsLAwtFotY8aMabqmsVQK09eCzEwUY4WiUTEGsLOQ8/AIb/YtHsv+58fwwFAvjifl8+C34Ty+KYMJtu/hbuHJRwkfESft2E5DqampeHt7NxmydjK5gIe/i8DF2oxf54/E17mur7q8vJwjR46ogK5uHP9QOr0QC4JQUl1dffLIkVuC74c+CfkJsOtpUTQawdnCmecGPkdseSx7Y/fWWmd6g8DHfybS3dGSh0e03C/cEObm5gQGBhIVFdVoUgFATEEM9++7n4sFF3l/9Pu8NfItqiurWyXCNZiamuLVy4vjZccZaeJHwLkt6Ac/AT3vaN3JVJUAglEWsUYvCrGptG47JVdbUZjzym+4TR7q8xAag4adl3c2eCyVSkVUVBQJCQkMGjSI3r17G+cWsHGDccvg8kG4fLhZMa4hyMOOd2f2JeKN21k7dyCe9pZ8fbSQmMh5WBn68H74+6w590WT32dr0Wq1ZGdnNxqyptUb+O38NZ7cfA4fZyt+fnYkHvb1CzRt2rRJrVar1wtCMzF4XXRaOr0QA+Tk5Cx///336/q+hjwBk96H+N9hz6ImW+oMVAwEQGIhISsrC4Dfoq5xKbecZZN7YWrSfpfB1dUVBwcHLl26VO89QRD4JekXHj34KCZSE7ZN3casgFmUlZW1SYRr+D7uezR6Da/kJ6K19yPM4k6SkpJat4hYm8zR/LS8VohldYW4Jpa4xk8M4G/vz0j3kfx86ec6xZuqqqqIjY3l3LlzdOvWjVGjRrX8WgyfD0494OAroFMbLcYA5nIZMwd2Y/vTw/niDkceGdwdXc7jaJRD+C5+E+M2P8uKg7EcjMslp7SqXYT5ypUr+Pr61rnR6A0CZ64U8frvsQz78G9e+jWaoG62/PT0iAaTiwwGA2vXri1TKpVft3lAXfzP6HRlMBtCEIRYDw+PrJSUFOeAgIAbb4x+HrRVcPwjkJvDtNUN+kLDssKQIGHWwFlcunAJeycFnx1OYoCXPdP6tX+6aq9evQgPDycnJ6c2HbZKV8UHZz9g75W9jO02lo/HfoydmV27iXC+Kp+fk37mLqkdfuVZ8PSvjFEEcfXqVU6dOoWTkxN+fn7Gh2C1QIhr4m9vFWJLU1FgNLq6N8l5gfN47shz/JX+F6McR3HlyhVUKhV+fn707du39b56E1OY8glsmw1n1sPYF2sjEc6ePcuIESNutNBqhJSUFPwUNsyY0Je39AZOXB7AVxe/4bJmJ1tSC9gQOg8M5jhbm9Hf0+6mhz3O1saHBlZVVZGbm0tISAiCIHAxU8ne6Gz2x+SQX67G0lTGpEBXpvf3YFwvlzrxwjezf/9+QaPRHBIEocHkpy7+GfwjhBigoKBg+aeffrp548aNdZ2F45aBVgWn1oCJBdz5YT0xDssKI8gpCDc7N8o8yli9/wJ5ZWrWPRDcIemqEomE4OBgTp8+jZWVFXn6PF47+RqXSy6zcOBCnu3/LFKJtN1EGODb2G/R67XMz4yDicvBvT8yxJoYPj4+5ObmcvHiRSQSCZ6enri7uzdT4Utyy3PjaPQapBJpvcLrOoNoNZrcUjd4qPNQPMw9+Dria5z9nPH398fR0bF9vouAidD7LghdBQPmgq2H0WKcl5dXGx4HYCKTMrGPGxP7vMOelIG8c3o53sFbuEvxNldyZcReK+VYUj41xrGHnTn9Pe3p52mHm605OoMBjV5Apzeg0wtoDdef9QauZedibmHF4T3xhF4u4FpJFaYyKeN7uTBjoAcTeiuwNG3+3/ODDz4ozM3N/aDtF66L/yX/GCHW6XR/7N27t/zjjz+2q9OVVyIROxhoq+DsesgIg2HPiNXF5BaUqkuJLYzlmf5i01A7V0+2X0hmYm8Xhvl23Gq4qakpXn28ePHwi0SqIrExtWH9xPWM9RTD7dpThHMqcth5+VdmVqjw8hoNIxfVeV8ikeDu7o67uzsqlYrMzExOnTqFhYUFrq6uKBSK+t2Va4rFa6ua/XytQVvPPwxitiKAVCKeb35+Pvn5+ej1eu7qdhcbr2zE3Ne8fpfltnLnh/DlMDj8Ftz7HUCzYlxSUkJiYiIjR45scOFsZsBMXCxdWHJsCWcqPueHe39ALpVTodYRn1VKzLVSYrJKib2m5GB8bpPDkwAyKZiaVCGXSRngZc+S23tyR5ArtubGLxpHR0dz9erVVEEQWhYP2EWn4x8jxIIg6K2trZcvX7589bp16+rG7kgkMHkFuAaKHXf3PCe2QB/0MGc8emIQDIz2GA3A+uOpaA1wt2/HFG4BMaHiu9jv+DHxRwyCgfE243nj9jdQ2Ihi0J4iDLAp5hvQ63i2UgvzNjRZY9jS0pJevXrRq1cvKioqyMvLIzo6GrVajY2NDfb29jg4OGCNHFMQZxvNoNara90SgiCgVqspLy8n/aoYpRIfG4NFqS2urq4MGjQICwsLgrXBbL+6nW2J2/jU5dM2X4M6OPjA6P9A6KfiWoKP+N03JsYVFRVcvHiR4cOHN+m6GOUxivdGvcfS0KV8EfUFLw15CWszE4b7OTHc78bNpFSlRVmlQS6TYiKTIJdef5ZJMZFKOHvmNP379zeqjGlTLF68uCg3N/f5Nh2ki07BP0aIASorKzf/8ssvbyxbtsy2Xs1WqRQGPwbBj4rJHpGb4Mx6wpzssbWxoV9pPrmmKraHX+WBYd1xMq2guLi4XWNENXoNOy7tYFPsJsrUZUzzm8aiQYuQVchIjknGaYQTlZWV7SrC18qv8XvyLu4tL8d92udgZ3z3Z2tra6ytrfH398dgMFBeXk5JSQmZmZloClIZCiTFR6NUeSGXy5HL5ZiYmCCRSKiuriYxMRGdTkd2XjYSvYTjx48DYGZmhrW1NTIT0bobHDyIYX51rV4ruRV397ibHYk7yBuch6tVO/cAHPMCRO+AA8vgmRMgE3/qt4qxIAicO3eO4ODg+rOCBpjsO5lzeefYHL+Zwa6DGe81vt42dpZy7CwbtmyvXr2KnZ1dm0U4NDSU5OTkGEEQItp0oC46Bf8oIRYEQS+Xy5csXbp0808//dRwVR6JBHzHgu9YDMpMTv0xm1GqCmQ/3oeVbQ9uZxpzhozAz8GU8+fPM3bsWKPKDjaFQTCwP3U/X174kuzKbEZ7jGbJ4CX0drzetNQaNBoNp0+fRqvVMnTo0HYRYYBvTr+PVDDwVLeJEHR3q48jlUqxs7O7Ea9b6Qlh0MOnG+r+/dFqtWg0mtr6yzKZDAcHB+RyORYFFliqLQkJCalzLYuS8oG0OvVyb+aB3g+wLWEbPyf9zPPB7WzYmVqKad2/PipWnRv2dO1bNWJ8+vRpJBIJffv2bTpO+RaWDl1KTEEMb4S9wa/Tf8XD2riWXGq1mitXrjBmzJjmN24CQRBYtGhRUW5u7oI2HaiLTsM/InztZnQ63R/Hjx/PSkxMbHbby4ZKCg3VjLntA7h7IxqNlg2ma+i7bwbWWSdxd3NrUz1hQRA4lXWKOX/M4fWw17Ezs2PTHZvYMGnDDRG+jr29PSqVChMTkzrdkNtCRkEcf+ScZo5aguu0Ne1yzFrk4hilumosLCywtbXF2dkZNzc33NzckMvluLm54eTkhCATMDMxq3dD0zeyWFeDl40X473G8+vlX6nWVTe4TZsInCmW/Dz6gVjA6CZsbGzQ6/Xo9foW3xTNZGasGrcKvaBn6YmlaPXGhQfGxsbSu3fvNrVBAtizZ48hPz//SJdv+N/DP06IBUEQ8vLy5i9evLjp1CzgUrEYyzvQbQgMuJ8XXTbwqeVLSLWVsGMuPU4sQJNwgLLS+hW3miO+KJ6n/3qa+X/Pp0JbwSdjP+Gnu35ihPuIetvW+IRHjRqFv78/4eHhbe6nh0HPxkPPYSoYePL21c3WDG4xJsYv1mn0mnqha3BT1ISscX/8w4EPo1Qr2XFpR+vG2RQSCUz5VOxGffT92pcrKysJDw8nODiYfv36GRVnfCvdbbvz7qh3iSmMYU1U8zfB3NxcBEFoc3cPvV7Pyy+/XJyXl/dimw7URafiHyfEAIIgnIqPj084e/asUdvLJDIEQSAuu4IC35nwXCTM+BJJZQH9ot9Bu2U2Bp1xwphZnsmyE8uYu28uScVJvDL0FfbO2stUv6lIJfUv560Lc926dautDXFzoZ4WIQio9v2Hv7SFTLcPwtl/UuuO0xRSKZiYg84IITZoGomaqLGIG/+ZDXUbynjP8Xwd/TW5lU1HG7QKRR8Y/iyc3wzZFykrKyMiIoKBAwfi6OjYoqSPW7nT507m9prLloQtHL16tNHt1Go1iYmJDTY2bSmbN2/WlpeX/yIIQlabD9ZFp+EfKcQAubm5C5577rmipjKcZBIxoUAQBPLK1BRVagjysBUXboIfhsXnYeLbOBWdI39f06GYxdXFrIhYwYzdMziWeYyn+z3Nn7P/ZF7gvAatQWg8OsLd3Z3AwEDOnDmDUtnCOHxBgL/e4kTSb1RJpUwZuaxl+7cEuUUbLWIxfE3WiGuihmXDlqE36Pns3GetG2dzjH8VrJzR7FlC1PXvw97evvbttojx0qFL6ePYhzdPvUlWRX1trKng1qdPn2aTSZqjurqa5cuXK/Pz81tQ3b+LfwL/WCEWBCEuOzs77ODBg43mNtckCOgFPXFZovuhb7ebFmVMTGHMiwgBk3CJ3UBxWky9Y6i0KjbGbGTqrqnsuLSDmf4z2T97P88HP4+NaePugOZC1JydnRk2bBjR0dEt6zYdugpOr+OAZx8UlgqCXYON37elyC2NCl9rTIhrfMTyJlwTIPqKn+r3FAfTD3I2x7hZTksQzGzJ678Q07wLjLHNavD7aK0Ym8pM+WzcZwiC0KC/OCMjA1NTU9zc3Np8Hl988UV1VVXVekEQ6lfh7+IfzT9WiAFyc3P/s2TJkmK9vuGiPzUWsQED8dllSCTQx/2WsCGJBMm0z5BKJRj2vYj6urtAZ9Dx6+Vfuev3u1h3YR3D3Ibx+4zfWT5qOQrLpgt4GxsnbGVlxahRo8jIyCApKan5+gVnN8CxDyjrdy9hOiWTfSY36A5pN9pqEV93TTRnEQM83vdxPK09+Tj8Y6MXv4xBr9dz8eJFchTjETwGY3LsPdFn3ACtFWMvWy/eG/0esYWxfB71ee3rpaWlZGRk0Ldv3zafh1Kp5PPPP1cWFRWtbPPBuuh0/KOFWBCEjJKSkh9XrVrVoFrUWMQGg4G47FJ8na2wMmsgYs/BG8ltb+BcFEnan19wJOMIs/fO5r0z79HNuhtbpmzhiwlf4GfffCubliZryOVyhg8fjl6vb9pvfGGbWMym910c7TcNrUHLFN8pzR6/TbRAiG8tgQk3pzg3/zMzNzHnteGvkVqayrbEbS0fawOUlZURFhaGvb09AwYOQjJ1JVTkwYnGE0haK8aTvCfxYO8H2ZqwlSNXj6DVarlw4QLBwcF1C9m3koULFyorKytfEwSh/TvVdvE/5x8txAAFBQWvrF69OicpqX4kz80WcXm1FusGRFgQBLR6LargR4nyCOSDos0sOb4EQRBYc9satkzZwiDFIKPG0tqMuZompAEBAZw5c6Z+cfn43WLzT7/b4N7vOZhxGE9rT4KcOq6ZJSBGThjjmjBokEvrh2Tpr/uIm4qauJkQzxDGe7V94U4QBNLT07lw4QKDBg3C19dXvCl7DoZB8+Ds11DYeNhia8X4pSEvEeQUxFun3uJw+GECAgLaJV78wIEDhqNHj0aXl5f/t80H66JT8o9K6GgIQRDUEolkzpw5cw5HRUU53lxSUHr9PrPoyCLKLHRUSNWE/CRDZ9ChE3Ro9Vp0wk2F5c3AWQdP2E/jnuCFdPfqbvQ42iNtWaFQYGdnx4ULF8jPz6dPnz6YpB2H354Cz6Ew90eKdZWczTnLE32f6JCCRXVoo2tCq286jrghXhn6CrP2zGLVuVWsGrfK+LFep7q6mpiYGMzMzBgzZkz9WsYTl0PCH3DgFZj3W6OdS1patQ1Ef/HKcSu5d8+9bMrZxK8jf23x+G+ltLSUZ555pjAvL2+u0BFFkbvoFPzjhRhAEITzCoVi66effvrMa6+9Vls5e6BiINP9pqMz6Ciq0BGWUkJ/Lw88HWyQS+XIpXJMpCa1z3blBUw+/BGmYyYSdiUVWxvbOqvrjdGetSPMzMwYPnw4GRkZxPyxgUHx7yNR9IYHfwFTK/66tA+9oGey7+Q2fY5RyC2hqtlw7UZdEwUVauQySYMzkcbwtPHkqX5Psf7ieu7pcQ8jPUYatV+NFZyRkUGfPn1wdW0kZdraBW57DQ6+Ckl/Qu9pjR6zNWIsK5fxqOJRvs75mtXnV/PKsFeMGn9jzJ8/X6lUKpcKgtABsX1ddBoEQfhXPAAzhUJxJTExUWgIpUoj+Ly6T1jz1+UG3xcEQRCKUgXhHVtBiNoqlJeXC0ePHhVUKlXj2wuCUFpaKhw9elQoKytrcrsWkxUlGD70EKo+DRLOhx6sHcejBx4VZv4+UzAYDO37eQ3xy2OC8MXgBt86duxY7d/DfxwurAhfUW+bZ7ZEChM/O97ij63WVQtTfpsi3LXrLkGj0zS7fWlpqXDy5EkhLi5O0Gq1zX+ATiMIXw4XhHVDBcGI65iXlyccP35cqK6ubnK74uJi4fjx44JGoxFWhK8Q+m7uK/yV/lfz42mE/fv3611dXY8BEqET/I91PTru8Y/3EdcgCII6Pz9/zpw5cxqMorCzkNPL1YbI9CYsPJvrWU9l2VhbWzNgwAAiIiIazYJr7ypqteRfgq2zkVg4Yv7MITx7DSI8PJxT0aeIyotisu/kjndLwPXwteZdEzdXX7uZKwWV+DkbWYj+JsxkZrw67FXSy9LZmri10e2qqqqIjo4mJiaGfv36ERQUZNzCmEwOI+ZDYRLkRDe7uTE+48rKSi5evMjQoUORy+W8OPhF+jr15e1Tb5NZntn8mG5BqVTWuCQeEAShyyXxL+dfI8Qguihyc3M3f/LJJw2uMA3zdSTqakltndx6yM3FHm1lYlyvo6MjPXr0ICIiglvFvcNEuDgNtswUxeKR3WDXDYVCQUhICJHlkQgIBMoC642nQ5A3v1hnEAzoDLp6rgmd3kBGUSX+CutWfXSIZwi3ed3GhugN9RbutFotCQkJhIeH4+LiwujRo1tUtAeAPjNAKoe4hnvn3UpTYlxdXU1kZCSDBg2qreAml8lZOW4lSODlEy/XtpMylmeeeUZZWlr6ktDlkvj/gn+VEAMUFBS8tnbt2pyGigIN9XFEpdETfa2JbDZbj1ohBvDw8MDT05Nz585huB4F0GEiXJYtirBeDQ/vBif/2rekUikRpRH0ceyDu5k7oaGhpKWl1VZD6xCMWKyr6Tt3q0WcWVKFVi+0yiKu4ZVhr2AQDKyMFENn1Wo1SUlJhIWFYWVlRUhICB4eHq2bHVg6QsDtELeryX6HN9OQGGs0GsLDwwkKCqq3nuBp48n7o98noSiBLQlbjB7avn37DKGhoVEVFRU/Gn9CXfyT+dcJsSAImvz8/PvmzJlTrNHUtULGBDjjaGXK0p0xlFY1kjRg262OEAN4e3vj5OREVFQUSqWyY0S4sgi2zBJ7xc37TSxyfxOZ5ZnEFsYy1XcqPXr0YMyYMeh0Ok6ePElCQgJVVc27EFqM3FKsNdGEUNX0q7s1fO1KfgVAqy1igG7W3Xi639MczjjM1pNbOXPmDObm5oSEhDTbgt4o+t0LZVlw9YzRu9wsxpWVlURERNCzZ09cXFwa3H6c5zhMJCaojAgDBCgqKmL+/PmFeXl5D3a5JP7/4V8nxACCIFzIycn57Kmnniq7+bfsYGXKhnmDySxWsWh7VMMuClsPKLtW7+WAgABMTU05deoUwcHB7SvC1aWw7W5QZsCDP0O3wfU2OZR+CBALzYCYCNKjRw/GjRuHra0tkZGRnD9/nvz8fNrt//d6KUyaKFFZM+W+1TWRWnhdiJ1bJ8R6vZ7s7GwCKwNRyBXsyNvBqDGjvNNHhAAAIABJREFU8Pb2rh+S1lp6TRFvNka6J2pQKBT06NGDY8eO4eXl1WRFtTxVHjpBRzfr5gv2a7Vapk6dWlJcXPykIAh5ze7Qxb+Gf6UQAxQVFX186NChI+vWraujIsN8HflwVj9OJhfywf4GahrbeUFVCagr6rxcVlZGUVER3bt3Jzk5udZN0WY0Kth+P+TFw5yt4NNw0fADaQcYpBiEu3Xdf3qpVIqnpydjx47F19eXnJwcjh8/Tnx8PGVlZW0bm/x6x4om3BM16ci3uiau5FfibG3aaKeKhhAEgaKiIi5evEhoaChKpZKB/QayPGQ5mZWZTS7ctQpTK1GM43dDC9KqtVotqamp+Pv7k56e3mTSR1a5WAjI08az2ePOnz+/LDU1da1Kpdpn9GC6+Ffwr4gjbghBEASJRPLABx98cD4oKKjPxIkTa286c4Z6cTmvnG/D0ujhas1Dw71v7Gh3vQVT6TVQiMXdb/UJp6SkEBkZyZAhQ9pmnWkq4ZdHIDMc7vkOet7R4GZXlFe4XHKZ14a91uihJBIJjo6OODo6otfrycvL49KlS6hUKpydnVEoFDg5ObVsvDUNRJsohdmoa6KgAj+X5q1hnU5HQUEBeXl5lJSUYGdnh5eXFwMGDKj1/Y61GcsErwl8E/MN0/ym4WbV9gI6tfS7D+J+gyvHGr3+N1NdXU1ERAQBAQF4eHjg5OTUZJzxtQpxdtWcRbx+/frqffv2nSgsLHyvdSfSxT+Zf60QQ23W3e3z5s2LOnXqlLuf341aEa9N7UNKQQXv7InH2syEGQOuL/rY1whxJih6N7gwFxAQgFwu5+zZswwbNqx1HRcyzsCehVCcCjPWQd/ZjW56IO0AUomUO3yaFwoQ2xh5eHjg4eGBXq+nsLCQ3NxcEhISsLCwwMnJCQcHB+zs7JoO9zLCItYYGnNNVHJnUP2kCo1Gg1KppKSkhKKiInQ6Hc7Oznh5edG/f/9G/b7Lhi1j1u5ZfBr5KavHr27mCrQA/4lgbi+6J5oRYpVKRUREBEFBQbU+4eaSPq6VX0MmkTV58zhx4oTw7rvvphUUFMzp8gv//8m/WogBBEHIlUgk0ydPnnzo/PnzTjViKpNK+OKBQTz8bTj/+ekiP569ytvT/1975x0fVZX+//fJlCSThPSOBJBEgYAkfANoCCCCimvBtSyCq9hXdBVsrLqLuiro2sCKnSKI8ANXLKDg0iS0EEqoCYEEQspM+kz6zJzfH3cSAySQhEAAz/v1Oq+5c+bOuefO3PnMuc95zvP0IrZ+RFx6+KTeEVFRURgMBpKTkxkwYACenp7HH7pp6qq01D0bPgC/LjD+x2bNEa7+szxrOQlhCQR5BrX6/HU6HaGhoQ0rzWw2LWlqTk4Ou3fvRkqJr68v3t7eeHl5NRSdTgdewQ2fBUHRTZ9OE6aJ4opaiitqifDRk5ubi81mw2q1YrVa0ev1DZmiu3Tp0uLPLdI7kgf6PsB7294j+WgyV0Re0erPokn0Ruh1o+Y9UVup5bprgtLSUrZt20a/fv3w9z82XeLJxPio7ShhXmHo3Zr+qWVlZXHHHXfkWyyWEVLKM5AvSnE+cMELMWj+xb6+vpNuvvnmGb/88ot//airk4eBJRMSWbDlMG/9ks4N7//GmP4RTHXTU2vOZKvt5N4REREReHh4sHHjRuLi4k69HDonBf77MBSma2neR74M7ie/fd9bvJfs8mzu6X1Pm879eOozN3fposXRcDgclJWVUVFRQVlZGbm5uVRUVOB0OtHX2RgMHNn8A0W2wGNG/tXV1ezevZu9Vs3OfjDjIPpsPXa7nYwSzcfZo7YUq1WHt7c3oaGh+Pj4nJanw/je4/nuwHdM2zyNxTcubjYgf6uJvRVS50D68ibvTPLz89m3bx8DBgzAy6tpd7zAoEC6Rndl5fqVxPaLReokNY4aMkszm7UP22w2rrnmmqK8vLzRUspWBKVWXGj8IYQYoKysbG5ISEjC5MmTx7/xxhsNyqpzE4wbGMX1fSN499cMZidnMcEQQOHu7fS89+lTekcEBASQkJBASkoK0dHRREY2YQu018Dq12D9dPCJgL9+CxcPb1G/lx9ajl7oGRE1onUn3EJ0Ol2Dbfl4pJTIPd0Il/l4R0Uds8IwNzeX4OBgctw0G+glF1/CgIgB6PV6zCk5sGknVw+6jKjAtvsRH49RZ+TZgc/y8MqHmbNnDvf3ub99Gu46GLzDNFtxIyGuqK3g7XVvc7T8KF5+XizcsJBKeyWVdZVU2auoqKugyl5FtaMau7ORP/dxC+nGXDLmhEM6nU5uueWW0oKCgqellJvb50QU5yt/GCEGsFgsE2fPnt0vLi5u0NixY48x7Pp6GvjX9b24sXcAJV8FIWz5DJm+kaExwYyKDeOqnqH4ejZtC/b29iYxMZHU1FTKysro2bPn74sMcrdro2DzHi0E4zVTwaNlq8Cc0snyrOVcEXkFvu6tXDnWDgghILI/+iObTrgdNxgMhISE4FmrmRZ8TD4NI+ZMiw2jzo3O/k3f5p8OgyMHM6LLCD7Z+Ql/6vanE7xI2oSbThPgLZ9BVSl4+mG325m6cipLLUsJMYVgKjVhMpgw6U0Em4Lx0nthMpjw0HvgrnPHQ+eBu94dd507tZW1FOUX0fuS3nh7eDcZRvW5556zbdu27evS0tIvT/8EFOc7fyghllI6hRDXT5w4cbOfn1+P66677hgXgvLycoqz9nLFoOtxX/8fXu+2m9dz4lixpwCDTpDYI4hRsWGM7BVGgNext8UGg4EBAwawb98+Nm7cSPxlfXDf9B6sexNMQVr0tJhrWtXfnZad5FXk8fe4v5/+ybeViDhtIstm0SKXHUeVy6Oi8WTdtiOl9AjxblFmjrbwTMIz3PjfG3kj5Y32m7iLvRU2fgh7v8caPZo1W9awongFI6NGtukYZrOZvXv3MmDQANyNx07gTZ8+veqLL77YYrFYOvCLVZxLXLB+xM0hpSy3WCyJ48ePP7Ry5coGZ+DGE3PuwydD1yRuPvoGyeODWTLhCu5J7MYBs43Ji9Po/8oKrp2+linf7eKHnbmYy7U5FiEEPXv2JMbPTu2HSbDmNYi9BSZsaLUIA/x06Cfcde4M79IyM8YZIcI1msvd1uTLGSUZ6ISOi3y0SU6ztZotWcWM6NVMGMp2INw7nAf7PsiK7BWsP7q+fRqNjAf/blSnzGPr1q3sdN9JjbOGR/s92qbmmotNMXPmzJqpU6emWiyWUVLKsxAwRHE+8IcTYgApZZHFYkkcN27c4bVr18oTvCN0erj1C/D0x23RXcQHC567rifrnrmSH/4+mEkjYgj2cef/bc3h0fnbGDD1V658czXPLkpl9zcvELDoZryd5ey97J/suXQiTo9TxzQ+HrvTzs9ZPzOk8xC8DO1nZ2014X0B0awQpxWm0cOvByaXq9vyXflICdf3bQeTwUm4u/fdRHWKYtrmaa0OqNMUdXY7eUGJuOduIuYSf5YcWsKfuv2pRemxmuN4MZ41a1bNlClTdro8JFqXLlpxQfOHFGIAKaXZbDYn3n777blz58490TvCOwRum635E3/7N3A6EUIQG+nLY1dFM/e+gez413B+HH8x7wx2cqtpO2N3P0DvvdP5qS6euzzeZZnXjWQU21m7bl2rV7mlFKRQXF185vPSnQp3HwiKaVKIndJJWmEafYL7NNT9uDOPHiHexIS24xLwJjDqjDw74Fmyy7NbFVCnKQoLC1m/fj1ul92OwMkXm1/D4XTwcL+HT7uf9WI8bdo0OXny5H0Wi+VK5aamOJ4/lI34eKSUuUKIy1955ZXkPn36RA4ZMuRYo2aXgXD1q1rSziX3a6JkzQdrHljzMdjM9EZSnzlOegaQNegDMu0Dqdhv5v1VB3BK6OSh57K0DYzrH87VA2Nb5MK1/NByTHoTSZFJZ+DMW0lkvLby7Diyy7Ox1lrpG9QX0MwSm7OK+fvwpn2O25vEyERGRo3k4x0fM6zzMHr492jV++vDaVZVVTFw4EA8PT3JWxnJ4tLd3Bxza4O55XRZvnx57cyZM/ebzeYkKWVFuzSquKD4QwsxgJTyiBBi4G233bZ+3rx5XUaMGHGsSg58CMy7IXUueAWBT5gWQD78Mu3RO1R79AlDBEXT1d2Hx4DHroqmtLKWdRmFrNpvZllaPuu+O0Ls+lwmDI9hVFy3ZsM31jnqWJG9guFdhuOh9zgLn8IpiIiDHV9DeR50+t3kkFaYBkCfIG1E/PNZMks05pmEZ9hu3s69P9/LzJEz6RXY65TvkVI2+Ab36NGDzp07N3wXG91qsaPjzp53tkv/Pv7445opU6bsNJvNVyoRVjRLR6cIOVcKEBIcHJzx448/2mVTOJqubiklFTXy/f9lyP4v/yKjJv8gh05dLhdsPCjtjhNT9azLWSdjZ8XKNUfWnNYx243Dm7QUUnt/aKhatWqVfHnDy3LgvIHS7vpsbp+Z3KbUSKdLdlm2HLlopLx83uVyW8G2k+5rtVrlhg0b5NatW09MfeRwyNdnRMn+sy9rOKfTYfr06ZXBwcHrAU95Dlzjqpy75Q9rIz4eKaXZYrEMGj9+/IH58+efGIrL7fRCL/qZjDxyZQ/W/2M4/7mlD0KnZ/K3e7jlvdUcLT52oFRQoUVAjPY7O7f4pyQ0FoTuBDtxWmEasYGx6Nx0DWaJ6/qcvdFwPV06dWHOqDkEeAbw4IoH2ZS36YR96urq2L17N6mpqURHRxMfH39ikJ7qUjINerob/dGdxvctpeTFF1+sfPXVVzdZLJbhUsozECxacSGhhLgRUvOmGDBx4sQNTz31lK3dQl02wl2v4/aELvzv6eG8dnMs+yxVXP3Oauat0eI+ADhcXk3NxSc46xhNENLzGCGuddaSXpzeMFHXEWaJxoR5hTHr2llEekcyYeUE1hxZA2hLuDMzM/ntt9/w8fEhKSmJwMDAphupKuGA0UC0qe3nUFlZyU033VT60UcffWOxWEZK5R2haAHnnRALIS4SQqwSQuwRQuwWQjzuqn9DCLFPCLFTCPGtEMLPVd9VCFElhNjuKjMbtTVMCJEihPhPfZ3U/IyvnDNnzhdXX311idVqPVPnwZiBUfz0+BC6Bvvw/LIs7v3wFw5m5+BwakLsJs6hryciThNi159FTm0OdmlvsA//mHZ2vCVORpBnEF9e8yXR/tFMXDWRuZvnsnbtWhwOB0lJSXTp0uWkaZXKynMw6/X08OnSpuPn5OSQkJBQvG7duucLCgrulVLaAYQQHkKIzUKIHa5r9iVX/aNCiANCCCmEaIjo5Louyxpds1MavTZGCJEqhJjYpk4qzknOoV96i7EDT0opewGDgEeEEL2AFUCslLIvkA40Dt6bKaXs5yp/a1T/MJAE6IQQl9ZXSimdZrP58S1btkzs379/UWZm5hk7me7B3nw7YTAPDe3O6iN27p63m9S9+wBwO5e+nog4LY1TmRZIIas2C4C+wX01s8ShjjFLHI+33pt/xvyTKGMUb+x9g6LwImJiYlqU3TmzWPvcL26DSSg5OVkOHDiwYP/+/TeVlJR8eNzLNcBwKeVlQD/gWiHEIGA9MALIbqLJdY2u2cYxiscACcAgIUTb81ApzinOoV96y5BS5kkpU13bVmAvECml/KV+BAJsBE6dEkE7fwk4gROGSmVlZXMyMjKuGTx4cN6vv/7a/nYKF0a9G8+O6slX9w+ktBZW5Wgj4g3JGzh48OAxwXY6jPoVdkdTAciuySbcK5wgzyB+3pWPswPNEqBFg9u3bx/r1q3DXbgz56Y5XB5xOS9teon5e+e3qI0DpdofbnTQqT0vGvP555/Xjh49OiM3N3eA3W7/7fjXpUZ9yheDq0gp5TYpZVarDvb7dSpp4ppVnJ+cd0LcGCFEVyAOOH525l5gWaPn3YQQ24QQa4QQjR1zPwOSATcpZRN5k7QQmvn5+fF33HHHnhkzZlTX23HPBIk9gvj6gUHUuiJ5dY6Jw+l08ttvv7Fz507OlJmkRYT21tLPu+zEWTVZ9Anqg9MpWZiS0yFmCSklxcXFbN26lc2bN+Pp6cmQIUOIjo6mk2cn3hv+HsMvGs60zdP4LO2zU7aXYcvBy+kkLCCmRce32+1MmDDB+txzz62xWCzxUsrDze0rhNAJIbYDZmCFlPLEGcVjudxlylgmhOjdqH4JkAKkuAYiiguBjnbbaGsBvIGtwJ+Pq38e+BYQrufuQKBruz9akMJObTiee0hIyJI777yztKamRp5Jpq5/T8bOipX9X/lJpueXS6fTKfPy8uSGDRvkunXrZFZWlqytrT2jfWiSmUOknHWDtFRaZOysWDlr1yw5f1O2jJr8g1ySeuSsdaOqqkpmZGTIVatWyZSUFFlYWCidzhPdAKWUstZRK59Z84yMnRUrZ2yd0ex+RVVF8s/zBstxM6Nb5KpYXFwsExMTi4ODg6fVX2stKYAfsArNjFZflwUENXreCfB2bV8HZLS0fVXOz3KOTMu3DiGEAVgMzJNSLmlUPx64HrhKuq5iqc1a17i2twohMoEYtFFFi5Fa2qVbli1b9mz//v2fXLhwYUDPnj3b54SOw99L+1oEbvzlk418dd9AekWEERYWRlVVFUeOHGH9+vV4eXkRGRlJaGho+2U2PhmR8ZC2mDTLTgCivC9l4uJ9DOwWwOh+p85S3GakpK4sj8ID2yg/vAtDZT7B+kq6u1Xj5hYLtsHgGw/6E3PGGdwMTB08FU+9J5+mfUqVvYpnEp5pmLQrrCpk1q4vWbjva2octTxrN5zSVXH16tXy7rvvLiwuLn7EarUuat2pyFIhxCrgWmBXM/uUN9r+SQjxoRAiSEpZ2JpjKc4fzjshFtov6HNgr5Ty7Ub11wLPAEOllJWN6oOBYimlQwjRHYgGDrbl2C5xnyqEWDZs2LBFjz32WPg//vEPU3uLYL372jcPJjLus03c+fkmFj40iB4hPnh6ehITE0N0dDRWq5WcnBzS09MxmUyEhYURGhraZBLLdiEiDlK+IO3wWtxw48ctbtiq7bw8Ovak3ghtpbKyEuvGOQQmv4zBbiMcaLBCu3cCT3/Y81/tuc4dOidA1BVauWiAlqUZ0LnpeOHyFzAZTMzdM5cqexUPX/Yws/fMZtG+b6h11nKdrYIH9WF0G/1+s/2pqKhg4sSJ5UuXLt1vNptvlScxRTTGdQ3WuUTYExgJvH6S/cOAAimlFEIMQDMhFrXkWIrzk/rb9/MGIcRgYB2QhjbJBvAc8C6aGaL+gt0opfybEOIW4N9AnWv/F6SU37dDP4zBwcHTwsLCxi9cuDDg0ksvPfWbWsi7qe/y+a7P2XHXDg4VVnDbzA3o3GDRQ1fQJfDEYOtSSmw2G/n5+RQUFOB0OgkMDCQ4OBh/f/+2JTdtiuJD8F4898f046Ddg4O7H+XBId157rr2uTOora2lqKgIi8VCcVER3XK/IyrjS5wR/XHre7uW48/vIi3Ttqcrol1lMRzeANnJkL0e8naAdIKbHgKjIaA7BHSDgO5I/258aNnAzPQFCARuwJ9slTxQUUfXoc9Dwn3NjobXrFkj77777qKysrJ/l5aWvi9b8cMRQvQFZgM6NFFdKKX8txDiMbTBQxia7fgnKeX9QohH0Tx67EAV8ISUMrmtn6vi3Oe8E+JzDSFEfEhIyKLHH388bPLkye0yOn5n6zvM3TOX1L9qHgr786385ZMN+HjoWfTQFYT5Nh9/Irs8m3xrPgXFBVhKLRSWF1LjrEHvoWf4RcPpFdELb2/vNueOc/73ERJLVqOvjKOu7B5WPjkUb/fW31g5HA7Ky8spKyujpKSEsrIyDAYDAQEBBAf4EbDxVdy2zdUCtt/0ARhaGHOjuhxyNmvCbN6nZckuOQT23wOefd3JlwMeHtxdXESXXrdouQN9mo6fXFFRwaRJk8q/++67dNcouClXM4XitFBC3A4IIYxBQUGvRURE3LVw4cLASy655LTaeyvlLRbsW8CWO7c01O3MKWXsp5sI7eTONw9dTpD3iWnb3976NiuyVzTbbqAxkBe6v4CoEggh8PLywsfHBy8vL0wmE56ennh4eJzUzJB5JJnR/3uImwoCGXTtfK7vG9Hsvk6nk+rqaiorK6msrMRms2Gz2aisrEQIQadOnfDz88PX1xc/Pz/tz6G6DBaNh8z/QdJTcOXzcBoJR10d0SLm1Yty8UGwFkC/sdCt+eh2a9eulXfddVdRWVnZy6Wlpe+1ZhSsULQGJcTtiBCif0hIyMJJkyaFP/30055tHR2/vvl1vj3wLRvHbjymfvOhYu76YhPdgrz5+oGB+JmMVNRV8FnaZ8zZPQedm457et9DXGgcnnpPTHqT9mgwccR6hHuX30t8aDwzR8xEIKioqMBqtVJRUUFlZSVVVVVUV/8+cjQajej1+obi5ubGT3mrmJv7Cd/m5CGHfkaNXw8cDgd2u72h1Ps9CyHw8PDAZDJhMpkahN9kMjUt9jYzzBkNhfvhhhlajr8OoLKykieeeKL822+/zXCNgrM6pCOKPwxKiNsZIYR7cHDw635+fuOmT58eMGrUKLfWTmRN2zSN7w9+T/IdJ5oF16ZbuH92ClFBHowdbmHO/o8orCrkhu438Fj8Y4R5hTXb7pKMJbyQ/AIP9HmAx+IfO2kfpJTU1dU1CKvdbsfpdDL2pxfJd2xi89Fc3DonUH79Z+h0ugaxNhgM6PX61k/e1VXD7BsgPw3GLoDuw1r3/nbA4XAwZ86cuilTppTabLappaWlM9QoWHE2OO+8Js51XO5yE4UQ79x3330zIiIiEj/44IOgQYMGtbgNh3RQba/m7ZS3udjvYnr49aCbbzdMBhNDYoJ5/hZ33kx5nbe3HyXGtzczrpxB3+C+p2z3z9F/ZodlB5+mfcplwZcx9KKhze4rhMBoNGI0/p4k9fsduRytzqBzpxjyugyi+6G5BFdmaF4Kp4OU8MNEzbZ7+5yzLsJSSpYuXep88skni61W6yKz2fxPKWXxWe2E4g+NGhGfYYQQsWFhYR/16tWr1/vvv98i3+O1OWuZkTqDQ2WHqHO6bvMRRHpHEuQZxHbLdgLdQyjPvZq68sv4YvwAEroGtKg/1fZq7lp2Fzm2HL65/psWZaGQUvLpuoNMXbYTn0te5J7Ye/m/sksZsv1xzYPhvl/gdNzXfpsOK1/Q7MFDn2l7O2059G+/8cgjjxSazebV+fn5k6SUOWe1AwoFSojPGkKIxNDQ0JlDhw7t/Oabb/pddNGpBdDutHPEeoQDpQc4UHqAzNJMjliPMLTzUMb3Hk+RFe7+cjNHS6p49444rundvFmiMTnWHG7/4XYivSOZO2ruSbOA2B1OXvx+N19tPExibCk7Ha/x3vD3IBOGeR/SRrJ/mQc9r2/xZ3EM+36CBWOh981awtYz4I/cFGlpaTz66KNF6enpafn5+Q9LKfedlQMrFE2ghPgsIoQQer3++sDAwBm33npr4EsvvdSp2di4LaS4opZ7Z21hZ04pk0bE8MCQ7ngYTj1JuDZnLY/8+ggjo0bynyH/aTL2cUWNnUfnp7Jqv4VxiSa21EzDVmtj2S3L2LZhG8OSBsOHA7Wg8Q8na9mvW0PBbvj8agiKhvE/aXGPzzBZWVk88cQTJcnJyYcLCgoekqeO+aBQnHHO66A/5xtSSllXV/d9QUFB9KxZsyb17t075/777y/LyMhoc5sBXkbmPzCQUX3CeWtFOle/s5afd+dzqj/YIZ2H8NT/PcWK7BVMXju5wQRST0F5Nbd/vIE16RYmXudNctW/qbJX8dk1n+Hr7qvtpNPDVVM0L4cdX7eu46VH4OsxYPSGMfPPuAhv2bKF0aNHF19++eXp33333diCgoI4JcKKc4aODnbxRy6ATq/X3xQeHr4tKSnJsmLFimaD0rSEdekWOfLt1TJq8g9y7Kcb5L688lO+Z9auWTJ2VqyctGqSrHVogYR2HCmRl09dKXv+a5n8cssamfh1ohz+zXB5oORAw/tWrVqlbTidUn5ypZRv9ZSytvLUnXQ6pUyZJeWrkVK+Ei7lkZS2nGqLqK2tlQsWLLDHxsZawsPD/wcMphUBelRR5WwVZZo4RxBC9AkPD5/i4eExdMKECZ3uuece97aYLewOJ/M3H+atX9KxVtdx56Aobo6LJDrUp9kVcLN2zeGtrW8QaUyg+uhYsgprCO3kzpM36nlrx2T8Pfz59OpPj5nYW716NcOGDdOeHFqruZ6FxkLcX6HPbeDVRN9Lj8DSv8PBVdA1CW58T1t+3M4cPnyYjz76qGLOnDkVdrt9sdlsfk22MC6EQtERKCE+xxBC+Hfq1Okek8n0aP/+/X2efPLJoGHDhrXaL7ekopbpK9P5atNhHE7tO+7s78kloT5Eh/pwSZiW3OHXvWbWpFuo9lyDR9j3+Mp+3BczhZDgw7ywaTKR3pF8MvITQr2OXQJ8jBADbPsKNn+ixXpwM0DMNdBvHESP1OI+bJ0Fv/xLiwNx9b+h/72nv2KuEXV1dSxdutT51ltvFWVlZRWUlJS8UV1dvUiqxJ2K8wAlxOcorihzCeHh4ZPd3NySrrvuOsOYMWP8kpKSWhXEJ6+sil1Hy0kvsLI/30p6gZVMi406h/a9B3kbGX5pCMMvDaWAX3lz62v0De7LnsI9RPtHM3PkTAI8TnSNO0GI68nfpdmLd34DFRYwBYF/FBzdCt2GwI3va8/bgYqKClauXMn8+fOL1q5da5dSfldQUPC2lHJ/uxxAoThLKCE+DxBCuANDIyIi7nI4HMPj4+MNd955Z+CoUaOEv79/q9urczjJKqygxu6kV3gn3Nx+H20v2LeAVze9SlxIHB9c9QE+xqazbjQrxPU46uDAStg+H/K2w+BJ0P+e03ZPy83NZenSpfavvvqqJDMzs9LpdP5gNpvnAZuldMUPVSjOM5QQn2e4Rsp9AwMD/2I0Gm8LCwvzHTduXKdP9AC8AAAD1UlEQVTRo0e7X3zxxe1yjMzSTDr7dMZd13xc41MKcTshpWTnzp0sXry4cuHChRVWqzXPZrPNKy8vXyylPHNZXRWKs4gS4vMcIUSEyWQa7e/vf5der+8eHx8vhg4d6puQkGDo168fJtOZcQs7U0JcUlLCtm3b2LRpU/WaNWusu3btksDO/Pz8Lx0OxzIpZUm7H1Sh6GCUEF9ACCGMQG+j0ZgQEhJylcPhiHd3d/ft168fSUlJfgMGDDD069cPb+/Tz8LeHkJcXFxMampqveiW7927VzgcjkIhxKa8vLxfpZRbgXRlclBc6CghvsBx5ffrrdfr/y80NHSE0+nsbzQafaOiomRUVJQuKirKo0uXLqaIiAgRERFBeHg4wcHBp8yBdyohrquro6CggNzcXPLy8sjNzXVmZ2dXZGdn1xw+fNh5+PBhHA5HIbApPz+/seg6m21UobhAUUL8B8QlzhFoKeDCjUZjpL+/f7TRaOwqpYy02+1BOp3O3cPDQxccHOz09PTEYDAIg8FQ/yhsNpu30Wi01tXVSVeoTGmz2YTFYhF1dXV2h8NRrdfrzUKInOrq6qyioqIMp9OZC+TVFyW6CoWGEmJFs7gEOwgtF6ABLWyq3rXtRMup1rhUAYXKlKBQtA4lxAqFQtHBqKA/CoVC0cEoIVYoFIoORgmxQqFQdDBKiBUKhaKDUUKsUCgUHYwSYoVCoehglBArFApFB6OEWNGAEOIiIcQqIcQeIcRuIcTjrvpvhBDbXSVLCLG90XueFUIcEELsF0Jc06h+jBAiVQgxsSPORaE4n2hl2l3FBY4deFJKmSqE8AG2CiFWSCn/Ur+DEOItoMy13QsYA/RGWzK9UggR41pZNwZIAOYJIbyllLazfTIKxfmCGhErGpBS5kkpU13bVmAvEFn/uisW8u1Afcrmm4AFUsoaKeUh4AAwoH73+mYbbSsUiiZQQqxoEiFEVyAOaJxyPgkokFJmuJ5HAkcavZ7D78K9BEgBUlyirlAomkGZJhQnIITwBhYDE6WU5Y1euoPfR8MnRUo5G5h9BrqnUFxwKCFWHIMr4tpiYJ6Uckmjej3wZ6B/o92PAhc1et7ZVadQKFqBMk0oGnDZgD8H9kop3z7u5RHAPillTqO6pcAYIYS7EKIbEA1sPju9VSguHNSIWNGYROCvQFojF7XnpJQ/oXlBHGOWkFLuFkIsBPageVw8omIRKxStR8UjVigUig5GmSYUCoWig1FCrFAoFB2MEmKFQqHoYJQQKxQKRQejhFihUCg6GCXECoVC0cEoIVYoFIoORgmxQqFQdDD/H7agYs6jNgqHAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(1, 1, 1, projection='polar')\n", "ax.plot(theta, r3, label='n=3')\n", "ax.plot(theta, r5, label='n=5')\n", "ax.plot(theta, r7, label='n=7')\n", "fig.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rappels sur les complexes\n", "\n", "Python et numpy gèrent nativement les complexes (le nombre imaginaire pur est noté $j$). Pour un complexe $z = a + bj = \\rho\\,e^{j\\theta}$, on a \n", "* `z = a + b * 1j` ou `z = rho * np.exp(1j * theta)`\n", "* parties réelle et imaginaire: `a = np.real(z)`, `b = np.imag(z)`, \n", "* module et argument: `rho = np.abs(z)`, `theta = np.angle(z)` (en radians)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z: (1+2j)\n", "Parties réelle et imaginaire: 1.0 2.0\n", "Module et argument: 2.23606797749979 1.1071487177940904\n" ] } ], "source": [ "z = 1 + 2j\n", "print(\"z:\", z)\n", "print(\"Parties réelle et imaginaire:\", np.real(z), np.imag(z))\n", "print(\"Module et argument:\", np.abs(z), np.angle(z))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Filtre passe-haut (diagramme de Bode)\n", "\n", "La fonction de transfert $H$ d'un filtre est définie comme le rapport entre le signal (complexe) de sortie $S$ et le signal (complexe) d'entrée $E$: $H = S/E$. $H$ est une grandeur complexe fonction de la pulsation $\\omega$, et dont le module donne le facteur d'atténuation/amplification (*gain*) et l'argument le déphasage entre les signaux de sortie et d'entrée (*phase*).\n", "\n", "Un filtre «passe-haut» permet de ne laisser passer que les signaux dont la pulsation $\\omega = 2\\pi f$ est supérieure à une valeur de coupure $\\omega_0$ et d'atténuer les signaux de fréquence inférieure.\n", "\n", "Nous voulons étudier le filtre passe-haut du 2e ordre dont la fonction de transfert complexe est:\n", "$$\n", "H_Q^{PH2}(x) = \\frac{-x^2}{1 - x^2 + j x/Q}\n", "$$\n", "\n", "où $x = \\omega/\\omega_0$ est la pulsation réduite, et $Q>0$ le facteur de qualité.\n", "\n", "Nous allons pour cela tracer son *diagramme de Bode*, constitué de deux graphiques représentant le comportement fréquentiel (en échelle logarithmique) de son gain (exprimé en dB) et de sa phase. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Définir une fonction `H_PH2(x, Q=1)` retournant la fonction de transfert complexe précédente (on choisit un facteur de qualité $Q=1$ par défaut)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def H_PH2(x, Q=1):\n", " \"\"\"\n", " Fonction de transfert complexe d'un filtre passe-haut du 2e ordre.\n", " \n", " x: pulsation réduite\n", " Q: facteur de qualité\n", " \"\"\"\n", " \n", " return -x**2 / (1 - x**2 + 1j * x / Q)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Définir une fonction `gain_dB(H)` retournant le gain en dB de la fonction de transfert complexe `H`: $G_{dB} = 20\\log_{10} |H|$. Pour la phase, utiliser directement la fonction `numpy.angle`." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def gain_dB(H):\n", " \"Gain en dB.\"\n", " \n", " return 20 * np.log10(np.abs(H))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Générer un vecteur $x$ de 100 points disposés logarithmiquement entre 0.1 et 10 \n", " ([numpy.logspace](https://numpy.org/doc/stable/reference/generated/numpy.logspace.html)).\n", "* Tracer dans 2 systèmes d'axes superposés (`plt.subplots(2, 1)`) le gain (en dB) et la phase (en radians) du filtre $H_Q^{PH2}(x)$ pour $Q=1/5$, $Q=1$ et $Q=5$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.logspace(-1, 1, 100)\n", "\n", "fig, (ax1, ax2) = plt.subplots(2, 1)\n", "\n", "# Gain [dB]\n", "ax1.plot(x, gain_dB(H_PH2(x, Q=0.2)), label='Q=1/5')\n", "ax1.plot(x, gain_dB(H_PH2(x, Q=1)), label='Q=1')\n", "ax1.plot(x, gain_dB(H_PH2(x, Q=5)), label='Q=5')\n", "\n", "# Phase [rad]\n", "ax2.plot(x, np.angle(H_PH2(x, Q=0.2)))\n", "ax2.plot(x, np.angle(H_PH2(x, Q=1)))\n", "ax2.plot(x, np.angle(H_PH2(x, Q=5)))\n", "\n", "ax1.set(ylabel='Gain [dB]', xscale='log', title='Filtre passe-haut du 2e ordre')\n", "ax2.set(xlabel=u'Pulsation réduite x', xscale='log', ylabel='Phase [rad]')\n", "ax1.legend()\n", "ax1.grid(which='both')\n", "ax2.grid(which='both')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Étalonnage d'un monochromateur avec une lampe à vapeur de mercure\n", "\n", "Un monochromateur est un dispositif optique permettant de mesurer ou de selectionner une longue d'onde précise d'un rayonnement. Il est constitué d'un système dispersif qui peut être un prisme ou un réseau. L'étalonnage d'un monochromateur a pour objectif de déterminer la relation $\\lambda = f(p)$ entre la position $p$ du système dispersif (p.ex. un angle) et la longueur d'onde $\\lambda$ du rayonnement.\n", "\n", "Le fichier [etalonnageMonochromateur.dat](etalonnageMonochromateur.dat) contient les données $p, \\lambda, \\delta p$ obtenues lors de l'étalonnage d'un monochromateur à l'aide d'une lampe à vapeur de mercure dont les longueurs d'onde sont connues.\n", "\n", "* Ouvrir le fichier [etalonnageMonochromateur.dat](etalonnageMonochromateur.dat) avec un éditeur de texte ou jupyter pour déterminer la strcuture du fichier (nombre, séparation, contenu des colonnes, commentaires, etc.).\n", "* Connaissant la structure du fichier, charger les données dans un tableau numpy avec \n", "[np.loadtxt](https://numpy.org/doc/stable/reference/generated/numpy.loadtxt.html). Quel est le format du tableau résultant?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(6, 3)\n" ] } ], "source": [ "# lecture des données à partir d'un fichier \"classique\" (séparation par des espaces, commentaires '#')\n", "data = np.loadtxt('etalonnageMonochromateur.dat')\n", "print(data.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Tracer les données $\\lambda = f(p)$ dans un graphique.\n", "\n", "**Rappel:** dans un tableau 2D, les lignes et les colonnes sont accessibles par *slice*, p.ex. `data[0]` et `data[:, 1]` donnent respectivement accès à la 1re ligne et 2e colonne du tableau `data`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "position = data[:, 0] # 1e colonne\n", "wavelength = data[:, 1] # 2e colonne\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "ax.scatter(position, wavelength, marker='+', s=50, label=u'Données')\n", "ax.set(title=u'Étalonnage monochromateur',\n", " xlabel='Position [u.a.]', ylabel = \"Longueur d'onde [nm]\")\n", "ax.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Étalonner le monochromateur consiste à déterminer une relation analytique approchant «au mieux» la relation entre les valeurs $(p_i, \\lambda_i)$ observée avec la lampe d'étalonnage. Une fois cette relation établie, elle permet de prédire la longueur d'onde correspondant à une position $p$ quelconque (dans le domaine de validité de la relation d'étalonnage). \n", "\n", "Compte tenu de la répartition linéaire des points $(\\lambda_i, p_i)$, la relation d'étalonnage sera obtenue en ajustant les données avec une *régression linéaire* $\\lambda = a p + b$ (utiliser \n", "[scipy.stats.linregress](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html#scipy.stats.linregress)):\n", "```python\n", "a, b, r_value, p_value, std_err = scipy.stats.linregress(x, y)\n", "```\n", "Le *coefficient de corrélation linéaire* $r$ (`r_value`) indique le degré de corrélation linéaire entre les deux variables ($-1 \\leq r \\leq +1$, on regarde en général le *coeff. de détermination* $r^2$). (Les deux autres paramètres `p_value` et `std_err` ne sont pas considérés ici.)\n", "\n", "* Déterminer et afficher l'équation de la droite d'étalonnage $\\lambda = a p + b$, ainsi que son coefficient de détermination $r^2$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Éq. de la droite d'étalonnage: lambda = 1.035 position -85.632 (r² = 1.000)\n" ] } ], "source": [ "a, b, r_value, p_value, std_err = scipy.stats.linregress(position, wavelength)\n", "print(\"Éq. de la droite d'étalonnage: lambda = {:.3f} position {:+.3f} (r² = {:.3f})\".format(a, b, r_value**2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Ajouter la droite d'étalonnage $\\lambda = a p + b$ à la figure précedente. Les longueurs d'onde seront calculées pour des valeurs de $p$ comprises entre 400 et 700.\n", "\n", " **Rappel:** en mode non-interactif(`%matplotlib inline`), si une figure `fig` existe déja, il est nécessaire de la réafficher (`fig`) après modification. En mode intéractif (`%matplotlib notebook`), la figure est automatiquement mise à jour au fur et à mesure." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = np.linspace(400, 700, 2)\n", "ax.plot(p, a * p + b, color='C1', label=r\"$\\lambda = {:.3f}\\times p {:+.3f}$ ($r^2 = {:.3f}$)\".format(a, b, r_value**2))\n", "ax.legend();\n", "ax.set(xlim=(400, 700))\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Pour aller plus loin:** \n", "Ajouter sur la figure les [barres d'erreur](https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.errorbar.html) $\\delta p$ sur la position $p$. En toute rigueur, il faudrait en tenir compte dans l'ajustement de la loi d'étalonnage (*moindres carrés pondérés*).\n", "\n", "Pour la lisibilité, vous devrez multiplier les barres d'erreur $\\delta p$ par un facteur multiplicatif pour les visualiser distinctement sur la figure. Ajouter cette information sur la figure.\n", "" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "errFactor = 300\n", "delta_p = data[:,2] * errFactor \n", "\n", "ax.errorbar(position, wavelength, xerr=delta_p, fmt='none', ecolor='C0', capsize=4, label=r\"$\\delta p$ ($\\times{})$\".format(errFactor))\n", "ax.legend()\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Le quartet d'Anscombe\n", "\n", "Nous allons charger et étudier 4 jeux de données $(x, y)$, d'abord en calculant des statistiques descriptives (moyennes, écarts type, etc.) puis en les visualisant.\n", "\n", "* Utiliser la fonction `numpy.loadtxt` pour charger les données du fichier [anscombe.dat](anscombe.dat) disponible depuis Claroline. Quel format (*shape*) a le tableau de retour?" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(11, 8)\n" ] } ], "source": [ "data = np.loadtxt('anscombe.dat')\n", "print(data.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Extraire du tableau précédent 4 jeux de données `j1` (les 2 premières colonnes), `j2` (les 2 suivantes), `j3` et `j4`, chacun de format $(11, 2)$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(11, 2)\n" ] } ], "source": [ "j1 = data[:, 0:2]\n", "j2 = data[:, 2:4]\n", "j3 = data[:, 4:6]\n", "j4 = data[:, 6:8]\n", "\n", "print(j1.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Pour chacun des 4 jeux de données `x, y = j.T`, calculer et afficher (avec 2 chiffres après la virgule) les statistiques suivantes:\n", " - les moyennes de $x$ et $y$ ([numpy.mean](https://numpy.org/doc/stable/reference/generated/numpy.mean.html)),\n", " - les écarts-type de $x$ et $y$ ([numpy.std](https://numpy.org/doc/stable/reference/generated/numpy.std.html)),\n", " - le coefficient de corrélation entre $x$ et $y$ ([scipy.stats.pearsonr](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html)),\n", " - l'équation de la droite de régression linéaire $y = ax + b$ \n", " ([scipy.stats.linregress](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.linregress.html)).\n", " \n", " Que constatez-vous? Que pouvez-vous en déduire?" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "============= Jeu #1 =============\n", "Moyennes: x=9.00, y=7.50\n", "Écarts-type: x=3.16, y=1.94\n", "Coeff. corrélation: r=0.82\n", "Rég. linéaire: a=0.50, b=3.00\n", "============= Jeu #2 =============\n", "Moyennes: x=9.00, y=7.50\n", "Écarts-type: x=3.16, y=1.94\n", "Coeff. corrélation: r=0.82\n", "Rég. linéaire: a=0.50, b=3.00\n", "============= Jeu #3 =============\n", "Moyennes: x=9.00, y=7.50\n", "Écarts-type: x=3.16, y=1.94\n", "Coeff. corrélation: r=0.82\n", "Rég. linéaire: a=0.50, b=3.00\n", "============= Jeu #4 =============\n", "Moyennes: x=9.00, y=7.50\n", "Écarts-type: x=3.16, y=1.94\n", "Coeff. corrélation: r=0.82\n", "Rég. linéaire: a=0.50, b=3.00\n" ] } ], "source": [ "for i, ji in enumerate([j1, j2, j3, j4], start=1):\n", " print(\" Jeu #{} \".format(i).center(34, '='))\n", " x, y = ji.T\n", " print(\"Moyennes: x={:.2f}, y={:.2f}\".format(np.mean(x), np.mean(y)))\n", " print(\"Écarts-type: x={:.2f}, y={:.2f}\".format(np.std(x), np.std(y)))\n", " r, _ = scipy.stats.pearsonr(x, y)\n", " print(\"Coeff. corrélation: r={:.2f}\".format(r))\n", " # slope, intercept, r_value, p_value, std_err\n", " a, b, _, _, _ = scipy.stats.linregress(x, y)\n", " print(\"Rég. linéaire: a={:.2f}, b={:.2f}\".format(a, b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Au sein d'une même figure (`plt.subplots(2, 2)`), tracer les 4 jeux de données $(x_i,y_i)$ (p.ex. `plot(x, y, 'bo')`), en y ajoutant à chaque fois la droite de régression linéaire (p.ex. `plot(x, a*x+b, 'r-')`). \n", "\n", " Que conclure?" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(2, 2, figsize=(8, 8), sharex=True, sharey=True) # retourne un tableau axs de format (2, 2)\n", "\n", "for i, ji in enumerate([j1, j2, j3, j4]):\n", " x, y = ji.T\n", " a, b, _, _, _ = scipy.stats.linregress(x, y)\n", " xx = np.array([x.min(), x.max()])\n", " \n", " axs[i//2, i%2].plot(x, y, ls='none', marker='o')\n", " axs[i//2, i%2].plot(xx, a*xx + b)\n", " axs[i//2, i%2].set(title=\"Jeu #{}\".format(i + 1))\n", "\n", "[ ax.set(xlabel='x') for ax in axs[1] ]\n", "[ ax.set(ylabel='y') for ax in axs[:, 0] ]\n", "fig.tight_layout()" ] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python3.6", "language": "python", "name": "python3.6" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.11" }, "toc": { "base_numbering": 1, "nav_menu": { "height": "210.667px", "width": "252px" }, "number_sections": false, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": "block", "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }